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University of Victoria
1.
Halverson-Duncan, Brittany.
The Representation Theory of the Symmetric Groups.
Degree: Department of Mathematics and Statistics, 2015, University of Victoria
URL: http://hdl.handle.net/1828/5931
► This paper forms an introductory account of the irreducible representations of the permutation group using Young Tableaux as the tool to achieve this. The basics…
(more)
▼ This paper forms an introductory account of the irreducible representations of the permutation group using
Young Tableaux as the tool to achieve this. The basics of C*-Algebra theory and
Young Tableaux are provided including a brief history of the two subjects. This paper provides a straightforward development of the
subject up to the main result which says that restricting the irreducible representations of S_n corresponding to the
Young diagrams of shape ? to S_n-1 decomposes as the direct sum of the irreducible representations of S_n-1 corresponding to the
Young diagrams formed by removing one box from ?.
Advisors/Committee Members: Putnam, Ian Fraser (supervisor), Emerson, Heath (supervisor).
Subjects/Keywords: permutation group; Young Tableaux
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APA (6th Edition):
Halverson-Duncan, B. (2015). The Representation Theory of the Symmetric Groups. (Masters Thesis). University of Victoria. Retrieved from http://hdl.handle.net/1828/5931
Chicago Manual of Style (16th Edition):
Halverson-Duncan, Brittany. “The Representation Theory of the Symmetric Groups.” 2015. Masters Thesis, University of Victoria. Accessed January 24, 2021.
http://hdl.handle.net/1828/5931.
MLA Handbook (7th Edition):
Halverson-Duncan, Brittany. “The Representation Theory of the Symmetric Groups.” 2015. Web. 24 Jan 2021.
Vancouver:
Halverson-Duncan B. The Representation Theory of the Symmetric Groups. [Internet] [Masters thesis]. University of Victoria; 2015. [cited 2021 Jan 24].
Available from: http://hdl.handle.net/1828/5931.
Council of Science Editors:
Halverson-Duncan B. The Representation Theory of the Symmetric Groups. [Masters Thesis]. University of Victoria; 2015. Available from: http://hdl.handle.net/1828/5931

Université du Québec à Montréal
2.
Serhan, Wiam.
Monoïde plaxique décalé et tableaux de Young.
Degree: 2015, Université du Québec à Montréal
URL: http://www.archipel.uqam.ca/8416/1/M14149.pdf
► Ce mémoire se concentre sur la théorie des tableaux de Young décalés. Nous introduisons un analogue décalé du monoïde plaxique de Lascoux et de Schützenberger,…
(more)
▼ Ce mémoire se concentre sur la théorie des tableaux de Young décalés. Nous introduisons un analogue décalé du monoïde plaxique de Lascoux et de Schützenberger, le monoïde plaxique décalé. Ce monoïde peut être défini de deux manières différentes soit par les relations de Knuth décalées, soit en utilisant l'insertion mixte de Haiman.
______________________________________________________________________________
MOTS-CLÉS DE L’AUTEUR : tableaux de Young, algorithme de Robinson-Schensted, jeu de taquin, monoïde plaxique, tableaux de Young décalés, insertion de Haiman.
Subjects/Keywords: Tableaux de Young; Monoïdes; Monoïde plaxique décalé; Analyse combinatoire
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❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
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APA (6th Edition):
Serhan, W. (2015). Monoïde plaxique décalé et tableaux de Young. (Thesis). Université du Québec à Montréal. Retrieved from http://www.archipel.uqam.ca/8416/1/M14149.pdf
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Serhan, Wiam. “Monoïde plaxique décalé et tableaux de Young.” 2015. Thesis, Université du Québec à Montréal. Accessed January 24, 2021.
http://www.archipel.uqam.ca/8416/1/M14149.pdf.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Serhan, Wiam. “Monoïde plaxique décalé et tableaux de Young.” 2015. Web. 24 Jan 2021.
Vancouver:
Serhan W. Monoïde plaxique décalé et tableaux de Young. [Internet] [Thesis]. Université du Québec à Montréal; 2015. [cited 2021 Jan 24].
Available from: http://www.archipel.uqam.ca/8416/1/M14149.pdf.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Serhan W. Monoïde plaxique décalé et tableaux de Young. [Thesis]. Université du Québec à Montréal; 2015. Available from: http://www.archipel.uqam.ca/8416/1/M14149.pdf
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Université du Québec à Montréal
3.
Serhan, Wiam.
Monoïde plaxique décalé et tableaux de Young.
Degree: 2015, Université du Québec à Montréal
URL: http://archipel.uqam.ca/8416/1/M14149.pdf
► Ce mémoire se concentre sur la théorie des tableaux de Young décalés. Nous introduisons un analogue décalé du monoïde plaxique de Lascoux et de Schützenberger,…
(more)
▼ Ce mémoire se concentre sur la théorie des tableaux de Young décalés. Nous introduisons un analogue décalé du monoïde plaxique de Lascoux et de Schützenberger, le monoïde plaxique décalé. Ce monoïde peut être défini de deux manières différentes soit par les relations de Knuth décalées, soit en utilisant l'insertion mixte de Haiman.
______________________________________________________________________________
MOTS-CLÉS DE L’AUTEUR : tableaux de Young, algorithme de Robinson-Schensted, jeu de taquin, monoïde plaxique, tableaux de Young décalés, insertion de Haiman.
Subjects/Keywords: Tableaux de Young; Monoïdes; Monoïde plaxique décalé; Analyse combinatoire
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❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Serhan, W. (2015). Monoïde plaxique décalé et tableaux de Young. (Thesis). Université du Québec à Montréal. Retrieved from http://archipel.uqam.ca/8416/1/M14149.pdf
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Serhan, Wiam. “Monoïde plaxique décalé et tableaux de Young.” 2015. Thesis, Université du Québec à Montréal. Accessed January 24, 2021.
http://archipel.uqam.ca/8416/1/M14149.pdf.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Serhan, Wiam. “Monoïde plaxique décalé et tableaux de Young.” 2015. Web. 24 Jan 2021.
Vancouver:
Serhan W. Monoïde plaxique décalé et tableaux de Young. [Internet] [Thesis]. Université du Québec à Montréal; 2015. [cited 2021 Jan 24].
Available from: http://archipel.uqam.ca/8416/1/M14149.pdf.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Serhan W. Monoïde plaxique décalé et tableaux de Young. [Thesis]. Université du Québec à Montréal; 2015. Available from: http://archipel.uqam.ca/8416/1/M14149.pdf
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of California – Berkeley
4.
Gillespie, Maria Monks.
A combinatorial approach to the q,t-symmetry in Macdonald polynomials.
Degree: Mathematics, 2016, University of California – Berkeley
URL: http://www.escholarship.org/uc/item/2729v8mg
► Using the combinatorial formula for the transformed Macdonald polynomials of Haglund, Haiman, and Loehr, we investigate the combinatorics of the symmetry relation Hmu(X;q,t)=Hmu*(X;t,q). We provide…
(more)
▼ Using the combinatorial formula for the transformed Macdonald polynomials of Haglund, Haiman, and Loehr, we investigate the combinatorics of the symmetry relation Hmu(X;q,t)=Hmu*(X;t,q). We provide a purely combinatorial proof of the relation in the case of Hall-Littlewood polynomials (q=0) when mu is a partition with at most three rows, and for the coefficients of the square-free monomials in X={x1,x2,...} for all shapes mu. We also provide a proof for the full relation in the case when mu is a hook shape, and for all shapes at the specialization t=1. Our work in the Hall-Littlewood case reveals a new recursive structure for the cocharge statistic on words.
Subjects/Keywords: Mathematics; Kostka polynomials; Macdonald polynomials; Mahonian statistics; q-analogs; Symmetric functions; Young tableaux
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❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Gillespie, M. M. (2016). A combinatorial approach to the q,t-symmetry in Macdonald polynomials. (Thesis). University of California – Berkeley. Retrieved from http://www.escholarship.org/uc/item/2729v8mg
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Gillespie, Maria Monks. “A combinatorial approach to the q,t-symmetry in Macdonald polynomials.” 2016. Thesis, University of California – Berkeley. Accessed January 24, 2021.
http://www.escholarship.org/uc/item/2729v8mg.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Gillespie, Maria Monks. “A combinatorial approach to the q,t-symmetry in Macdonald polynomials.” 2016. Web. 24 Jan 2021.
Vancouver:
Gillespie MM. A combinatorial approach to the q,t-symmetry in Macdonald polynomials. [Internet] [Thesis]. University of California – Berkeley; 2016. [cited 2021 Jan 24].
Available from: http://www.escholarship.org/uc/item/2729v8mg.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Gillespie MM. A combinatorial approach to the q,t-symmetry in Macdonald polynomials. [Thesis]. University of California – Berkeley; 2016. Available from: http://www.escholarship.org/uc/item/2729v8mg
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Northeastern University
5.
Singh, Rahul.
Orbital Varieties, And Conormal Varieties To Schubert Varieties.
Degree: PhD, Department of Mathematics, 2019, Northeastern University
URL: http://hdl.handle.net/2047/D20317966
► Schubert varieties, being the foundational objects of enumerative geometry, have been studied by mathematicians for over a century. Their conormal varieties, and the closely related…
(more)
▼ Schubert varieties, being the foundational objects of enumerative geometry, have been studied by mathematicians for over a century. Their conormal varieties, and the closely related orbital varieties, have come to play a key role in the representation theory of Lie algebras and algebraic groups. While the combinatorics, and the associated representation theory, of these objects is somewhat well-understood, little is known about their local geometry. In this dissertation, we study primarily the conormal varieties of Schubert varieties in a cominuscule Grassmannian, and the associated orbital varieties. We first show that a compactification given by Lakshmibai, Ravikumar, and Slofstra, identifying the cotangent bundle of the Grassmannian with an open subset of an affine Schubert variety, is the best possible in type A, and does not extend to partial flag varieties. By studying the images of conormal varieties under this compactification, we show that certain conormal varieties can be identified as open subsets of certain affine Schubert varieties, and hence are normal, Cohen-Macaulay, and compatibly Frobenius split. As a corollary, this allows us to compute the projective dual of various determinantal varieties. Next, we mimic the above compactification to show that the conormal varieties of certain Schubert divisors (namely those corresponding to long roots) in a general flag variety can be identified as open subsets of certain affine Schubert varieties. We also show that the same is true for orbital varieties of minimal shape. Finally, we construct a resolution of singularities, and in types A and C, compute a system of defining equations, for the conormal variety of any Schubert subvariety of a cominuscule Grassmannian. As a corollary, this recovers a known system of defining equations for two-column orbital varieties, and also suggests a natural, type-independent, conjecture that could be a first step towards obtaining a system of defining equations in other cominuscule cases.
Subjects/Keywords: Conormal Varieties; Loop Groups; Orbital Varieties; Schubert Varieties; Steinberg Variety; Young Tableaux; Mathematics
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❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Singh, R. (2019). Orbital Varieties, And Conormal Varieties To Schubert Varieties. (Doctoral Dissertation). Northeastern University. Retrieved from http://hdl.handle.net/2047/D20317966
Chicago Manual of Style (16th Edition):
Singh, Rahul. “Orbital Varieties, And Conormal Varieties To Schubert Varieties.” 2019. Doctoral Dissertation, Northeastern University. Accessed January 24, 2021.
http://hdl.handle.net/2047/D20317966.
MLA Handbook (7th Edition):
Singh, Rahul. “Orbital Varieties, And Conormal Varieties To Schubert Varieties.” 2019. Web. 24 Jan 2021.
Vancouver:
Singh R. Orbital Varieties, And Conormal Varieties To Schubert Varieties. [Internet] [Doctoral dissertation]. Northeastern University; 2019. [cited 2021 Jan 24].
Available from: http://hdl.handle.net/2047/D20317966.
Council of Science Editors:
Singh R. Orbital Varieties, And Conormal Varieties To Schubert Varieties. [Doctoral Dissertation]. Northeastern University; 2019. Available from: http://hdl.handle.net/2047/D20317966

University of Kentucky
6.
Sawyer, Kalila Joelle.
Scrollar Invariants of Tropical Chains of Loops.
Degree: 2020, University of Kentucky
URL: https://uknowledge.uky.edu/math_etds/68
► We define scrollar invariants of tropical curves with a fixed divisor of rank 1. We examine the behavior of scrollar invariants under specialization, and compute…
(more)
▼ We define scrollar invariants of tropical curves with a fixed divisor of rank 1. We examine the behavior of scrollar invariants under specialization, and compute these invariants for a much-studied family of tropical curves. Our examples highlight many parallels between the classical and tropical theories, but also point to some substantive distinctions.
Subjects/Keywords: tropical geometry; divisor theory; scrollar invariants; Maroni invariant; young tableaux; Algebraic Geometry
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APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Sawyer, K. J. (2020). Scrollar Invariants of Tropical Chains of Loops. (Doctoral Dissertation). University of Kentucky. Retrieved from https://uknowledge.uky.edu/math_etds/68
Chicago Manual of Style (16th Edition):
Sawyer, Kalila Joelle. “Scrollar Invariants of Tropical Chains of Loops.” 2020. Doctoral Dissertation, University of Kentucky. Accessed January 24, 2021.
https://uknowledge.uky.edu/math_etds/68.
MLA Handbook (7th Edition):
Sawyer, Kalila Joelle. “Scrollar Invariants of Tropical Chains of Loops.” 2020. Web. 24 Jan 2021.
Vancouver:
Sawyer KJ. Scrollar Invariants of Tropical Chains of Loops. [Internet] [Doctoral dissertation]. University of Kentucky; 2020. [cited 2021 Jan 24].
Available from: https://uknowledge.uky.edu/math_etds/68.
Council of Science Editors:
Sawyer KJ. Scrollar Invariants of Tropical Chains of Loops. [Doctoral Dissertation]. University of Kentucky; 2020. Available from: https://uknowledge.uky.edu/math_etds/68
7.
Khlifi, Olfa.
Le cône diamant : Diamond cone.
Degree: Docteur es, Mathématiques, 2010, Dijon; Université de Sfax (Tunisie)
URL: http://www.theses.fr/2010DIJOS080
► Le cône diamant a été introduit par N. J. Wildberger pour l'algèbre de Lie sl(n;R). C'est une présentation combinatoire d'une base de l'espace C[N] des…
(more)
▼ Le cône diamant a été introduit par N. J. Wildberger pour l'algèbre de Lie sl(n;R). C'est une présentation combinatoire d'une base de l'espace C[N] des fonctions polynomiales sur le facteur nilpotent N de la décompositon d'Iwasawa de SL(n;R), qui respecte la stratification naturelle de ce N-module indécomposable. Cette approche combinatoire peut se réaliser à l'aide de tableaux de Young, qui indexent une telle base. On réalise l'algèbre C[N] comme un quotient, appelé algèbre de forme réduite, de l'algèbre de forme S_ de SL(n;R), on en déduit une base indexée par des tableaux de Young semi standards particuliers, dits tableaux quasi standards. Dans cette thèse cette construction est étendue aux cas des algèbres semi simples de rang 2, puis des algèbres sp(2n), enfin aux super algèbres de Lie sl(m; 1). Dans chaque cas, on définit les tableaux quasi standards, et on montre qu'ils forment une bonne base de l'algèbre de forme réduite, soit directement, soit en utilisant une variante du jeu de taquin de Schützenberger.
The diamond cone was introduced by N. J. Wildberger for the Lie algebra sl(n;R). It is a combinatoric presentation for the space C[N] of polynomials functions on the nilpotent factor N in the Iwasawa decomposition of SL(n;R). This presentation describes the natural layering of this indecomposable N-module. This basis can be indexeded by using some semi standard Young tableaux. We realize the algebra C[N] as a quotient of the shape algebra S_ for SL(n;R). Let us call reduced shape algebra this quotient. It is possible to select a family of semi standard Young tableaux, the quasi standard tableaux, in such a manner to get a basis for the reduced shape algebra. In the present thesis, this construction is extended to the case of rank 2 semi simple Lie algebras, then to the cas of the Lie algebras sp(2n), finally, to the case of the super simple Lie algebra sl(m; 1). In each case, we define the quasi standard Young tableaux, and show they define a good basis for the reduced shape algebra, either directly, or using an adapted version of the jeu de taquin defined by Schützenberger.
Advisors/Committee Members: Arnal, Didier (thesis director), Agrebaoui, Boujemaâ (thesis director).
Subjects/Keywords: Algèbres de Lie semi simples et nilpotentes; Représentations et algèbre de forme; Tableaux de Young; Tableaux semi standards et quasi standards; No english keywords; 512
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❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Khlifi, O. (2010). Le cône diamant : Diamond cone. (Doctoral Dissertation). Dijon; Université de Sfax (Tunisie). Retrieved from http://www.theses.fr/2010DIJOS080
Chicago Manual of Style (16th Edition):
Khlifi, Olfa. “Le cône diamant : Diamond cone.” 2010. Doctoral Dissertation, Dijon; Université de Sfax (Tunisie). Accessed January 24, 2021.
http://www.theses.fr/2010DIJOS080.
MLA Handbook (7th Edition):
Khlifi, Olfa. “Le cône diamant : Diamond cone.” 2010. Web. 24 Jan 2021.
Vancouver:
Khlifi O. Le cône diamant : Diamond cone. [Internet] [Doctoral dissertation]. Dijon; Université de Sfax (Tunisie); 2010. [cited 2021 Jan 24].
Available from: http://www.theses.fr/2010DIJOS080.
Council of Science Editors:
Khlifi O. Le cône diamant : Diamond cone. [Doctoral Dissertation]. Dijon; Université de Sfax (Tunisie); 2010. Available from: http://www.theses.fr/2010DIJOS080
8.
Barns-Graham, Alexander Edward.
Much ado about nothing : the superconformal index and Hilbert series of three dimensional N =4 vacua.
Degree: PhD, 2019, University of Cambridge
URL: https://doi.org/10.17863/CAM.35266
;
https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.763880
► We study a quantum mechanical σ-model whose target space is a hyperKähler cone. As shown by Singleton, [184], such a theory has superconformal invariance under…
(more)
▼ We study a quantum mechanical σ-model whose target space is a hyperKähler cone. As shown by Singleton, [184], such a theory has superconformal invariance under the algebra \mathfrak{osp}(4^*|4). One can formally define a superconformal index that counts the short representations of the algebra. When the hyperKähler cone has a projective symplectic resolution, we define a regularised superconformal index. The index is defined as the equivariant Hirzebruch index of the Dolbeault cohomology of the resolution, hereafter referred to as the index. In many cases, the index can be explicitly calculated via localisation theorems. By limiting to zero the fugacities in the index corresponding to an isometry, one forms the index of the submanifold of the target space invariant under that isometry. There is a limit of the fugacities that gives the Hilbert series of the target space, and often there is another limit of the parameters that produces the Poincaré polynomial for ℂ^ × -equivariant Borel-Moore homology of the space. A natural class of hyperKähler cones are Nakajima quiver varieties. We compute the index of the A-type quiver varieties by making use of the fact that they are submanifolds of instanton moduli space invariant under an isometry. Every Nakajima quiver variety arises as the Higgs branch of a three dimensional \mathcal N =4 quiver gauge theory, or equivalently the Coulomb branch of the mirror dual theory. We show the equivalence between the descriptions of the Hilbert series of a line bundle on the ADHM quiver variety via localisation, and via Hanany's monopole formula. Finally, we study the action of the Poisson algebra of the coordinate ring on the Hilbert series of line bundles. We restrict to the case of looking at the Coulomb branch of balanced ADE-type quivers in a certain infinite rank limit. In this limit, the Poisson algebra is a semiclassical limit of the Yangian of ADE-type. The space of global sections of the line bundle is a graded representation of the Poisson algebra. We find that, as a representation, it is a tensor product of the space of holomorphic functions with a finite dimensional representation. This finite dimensional representation is a tensor product of two irreducible representations of the Yangian, defined by the choice of line bundle. We find a striking duality between the characters of these finite dimensional representations and the generating function for Poincaré polynomials.
Subjects/Keywords: 530.12; quantum mechanics; superconformal; complex geometry; yangian; quantum group; young tableaux; quantum field theory; string theory; sheaf cohomology
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❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Barns-Graham, A. E. (2019). Much ado about nothing : the superconformal index and Hilbert series of three dimensional N =4 vacua. (Doctoral Dissertation). University of Cambridge. Retrieved from https://doi.org/10.17863/CAM.35266 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.763880
Chicago Manual of Style (16th Edition):
Barns-Graham, Alexander Edward. “Much ado about nothing : the superconformal index and Hilbert series of three dimensional N =4 vacua.” 2019. Doctoral Dissertation, University of Cambridge. Accessed January 24, 2021.
https://doi.org/10.17863/CAM.35266 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.763880.
MLA Handbook (7th Edition):
Barns-Graham, Alexander Edward. “Much ado about nothing : the superconformal index and Hilbert series of three dimensional N =4 vacua.” 2019. Web. 24 Jan 2021.
Vancouver:
Barns-Graham AE. Much ado about nothing : the superconformal index and Hilbert series of three dimensional N =4 vacua. [Internet] [Doctoral dissertation]. University of Cambridge; 2019. [cited 2021 Jan 24].
Available from: https://doi.org/10.17863/CAM.35266 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.763880.
Council of Science Editors:
Barns-Graham AE. Much ado about nothing : the superconformal index and Hilbert series of three dimensional N =4 vacua. [Doctoral Dissertation]. University of Cambridge; 2019. Available from: https://doi.org/10.17863/CAM.35266 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.763880
9.
Poulain d andecy, Loic.
Algèbres de Hecke cyclotomiques : représentations, fusion et limite classique. : Cooperation among financial supervisors in the European Union.
Degree: Docteur es, Physique théorique et mathématique, 2012, Aix Marseille Université
URL: http://www.theses.fr/2012AIXM4036
► Une approche inductive est développée pour la théorie des représentations de la chaîne des algèbres de Hecke cyclotomiques de type G(m,1,n). Cette approche repose sur…
(more)
▼ Une approche inductive est développée pour la théorie des représentations de la chaîne des algèbres de Hecke cyclotomiques de type G(m,1,n). Cette approche repose sur l'étude du spectre d'une famille commutative maximale, formée par les analogues des éléments de Jucys – Murphy.Les représentations irréductibles, paramétrées par les multi-partitions, sont construites avec l'aide d'une nouvelle algèbre associative, dont l'espace vectoriel sous-jacent est le produit tensoriel de l'algèbre de Hecke cyclotomique avec l'algèbre associative libre engendrée par les multi-tableaux standards.L'analogue de cette approche est présentée pour la limite classique, c'est-à-dire la chaîne des groupes de réflexions complexes de type G(m,1,n).Dans une seconde partie, une base des algèbres de Hecke cyclotomiques est donnée et la platitude de la déformation est montrée sans utiliser la théorie des représentations. Ces résultats sont généralisés aux algèbres de Hecke affines de type A.Ensuite, une procédure de fusion est présentée pour les groupes de réflexions complexes et les algèbres de Hecke cyclotomiques de type G(m,1,n). Dans les deux cas, un ensemble complet d'idempotents primitifs orthogonaux est obtenu par évaluation consécutive d'une fonction rationnelle.Dans une troisième partie, une nouvelle présentation est obtenue pour les sous-groupes alternés de tous les groupes de Coxeter. Les générateurs sont reliés aux arêtes orientées du graphe de Coxeter. Cette présentation est ensuite étendue, pour tous les types, aux extensions spinorielles des groupes alternés, aux algèbres de Hecke alternées et aux sous-groupes alternés des groupes de tresses.
An inductive approach to the representation theory of the chain of the cyclotomic Hecke algebras of type G(m,1,n) is developed. This approach relies on the study of the spectrum of a maximal commutative family formed by the analogues of the Jucys – Murphy elements.The irreducible representations, labelled by the multi-partitions, are constructed with the help of a new associative algebra, whose underlying vector space is the tensor product of the cyclotomic Hecke algebra with the free associative algebra generated by the standard multi-tableaux.The analogue of this approach is presented for the classical limit, that is for the chain of complex reflection groups of type G(m,1,n).In a second part, a basis of the cyclotomic Hecke algebras is given and the flatness of the deformation is proved without using the representation theory. These results are extended to the affine Hecke algebras of type A.Then a fusion procedure is presented for the complex reflection groups and the cyclotomic Hecke algebras of type G(m,1,n). In both cases, a complete set of primitive orthogonal idempotents is obtained by successive evaluations of a rational fonction.In a third part, a new presentation is obtained for the alternating subgroups of all Coxeter groups. The generators are related to oriented edges of the Coxeter graph. This presentation is then extended, for all types, to the spinor extensions of the…
Advisors/Committee Members: Ogievetsky, Oleg (thesis director).
Subjects/Keywords: Groupes de tresses; Algèbres de Hecke; Groupes de réflexions; Théorie des représentations; Éléments de Jucys – Murphy; Diagrammes et tableaux de Young; Diagrammes de Bratteli; Procédures de fusion; Algorithme de Coxeter-Todd; Sous-groupes alternés; Braid groups; Hecke algebras; Reflection groups; Representation theory; Jucys – Murphy elements; Young diagrams and Young tableaux; Bratteli diagrams; Fusion procedures; Coxeter-Todd algorithm; Alternating subgroups
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APA ·
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MLA ·
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APA (6th Edition):
Poulain d andecy, L. (2012). Algèbres de Hecke cyclotomiques : représentations, fusion et limite classique. : Cooperation among financial supervisors in the European Union. (Doctoral Dissertation). Aix Marseille Université. Retrieved from http://www.theses.fr/2012AIXM4036
Chicago Manual of Style (16th Edition):
Poulain d andecy, Loic. “Algèbres de Hecke cyclotomiques : représentations, fusion et limite classique. : Cooperation among financial supervisors in the European Union.” 2012. Doctoral Dissertation, Aix Marseille Université. Accessed January 24, 2021.
http://www.theses.fr/2012AIXM4036.
MLA Handbook (7th Edition):
Poulain d andecy, Loic. “Algèbres de Hecke cyclotomiques : représentations, fusion et limite classique. : Cooperation among financial supervisors in the European Union.” 2012. Web. 24 Jan 2021.
Vancouver:
Poulain d andecy L. Algèbres de Hecke cyclotomiques : représentations, fusion et limite classique. : Cooperation among financial supervisors in the European Union. [Internet] [Doctoral dissertation]. Aix Marseille Université 2012. [cited 2021 Jan 24].
Available from: http://www.theses.fr/2012AIXM4036.
Council of Science Editors:
Poulain d andecy L. Algèbres de Hecke cyclotomiques : représentations, fusion et limite classique. : Cooperation among financial supervisors in the European Union. [Doctoral Dissertation]. Aix Marseille Université 2012. Available from: http://www.theses.fr/2012AIXM4036

Universidade de Lisboa
10.
Rodrigues, Inês Martins.
Estruturas combinatórias associadas aos coeficientes de Littlewood-Richardson.
Degree: 2015, Universidade de Lisboa
URL: http://www.rcaap.pt/detail.jsp?id=oai:repositorio.ul.pt:10451/23616
► Tese de mestrado em Matemática, apresentada à Universidade de Lisboa, através da Faculdade de Ciências, 2015
Os coeficientes de Littlewood-Richardson surgem inicialmente no contexto das…
(more)
▼ Tese de mestrado em Matemática, apresentada à Universidade de Lisboa, através da Faculdade de Ciências, 2015
Os coeficientes de Littlewood-Richardson surgem inicialmente no contexto das funções de Schur. A primeira regra para os determinar foi apresentada por Littlewood e Richardson, nos anos trinta, e descreve-os como contando certos tipos de tableaux de Young enviesados. Contudo, só mais tarde, no final dos anos setenta, foi apresentada uma demonstração rigorosa, por Schützenberger e Thomas - baseada na teoria entretanto desenvolvida em torno de tableaux de Young, em particular a correspondência RSK e o jeu de taquin. Mais recentemente, a partir dos anos oitenta, têm sido apresentadas outras interpretações combinatórias para estes coeficientes, bem como demonstrações mais simples da regra de Littlewood-Richardson. O objectivo desta dissertação passa por apresentar tanto uma abordagem clássica aos coeficientes de Littlewood-Richardson, como também expor várias outras interpretações mais recentes, tornando claras as correspondências entre elas. Destacamos os padrões de Gelfand-Tsetlin, as colmeias de Knutsen e Tao, e os triângulos de Berenstein-Zelevinsky. Para além de uma breve referência a tableaux de Young e alguns dos seus algoritmos combinatórios mais importantes, nesta dissertação serão apresentadas os principais resultados relativos a funções de Schur; evidenciamos a sua relação com tableaux e observamos que formam uma base para a álgebra das funções simétricas. O produto de funções de Schur, bem como as funções de Schur indexadas por formas enviesadas, motivam a introdução dos coeficientes de Littlewood-Richardson, como sendo os coeficientes que aparecem numa combinação linear de outras funções de Schur. Segue-se a apresentação da abordagem clássica à regra de Littlewood-Richardson: enunciada em termos de certos tipos de tableaux enviesados e demonstrada com recurso ao jeu de taquin. Será também apresentada uma demonstração mais recente, que se baseia nas involuções de Bender-Knuth, inicialmente utilizadas na demonstração da simetria das funções de Schur. Para concluir, serão apresentadas algumas estruturas combinatórias mais recentes que são também contadas pelos coeficientes de Littlewood-Richardson, estabelecendo-se bijecções entre elas.
The Littlewood-Richardson coefficients initially emerge in the context of Schur functions. The first rule to determine them was presented by Littlewood and Richardson, during the thirties, and describe them as counting certain types of skew Young tableaux. However, it was only in the late seventies that a rigorous proof was presented, by Schützenberger and Thomas - based on the theory regarding Young tableaux developed in the meantime, particularly the RSK correspondence and jeu de taquin. More recently, from the eighties, other combinatorial interpretations for these coefficients have been presented, as well as other simpler proof for the Littlewood-Richardson rule. The purpose of this thesis is to present a classical approach to the Littlewood-Richardson…
Advisors/Committee Members: Torres, Maria Manuel Correia,1969-.
Subjects/Keywords: Partições; Tableaux de Young; Funções simétricas; Funções de Schur; Coeficientes de Littlewood-Richardson; Teses de mestrado - 2015; Domínio/Área Científica::Ciências Naturais::Matemáticas
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APA ·
Chicago ·
MLA ·
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CSE |
Export
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APA (6th Edition):
Rodrigues, I. M. (2015). Estruturas combinatórias associadas aos coeficientes de Littlewood-Richardson. (Thesis). Universidade de Lisboa. Retrieved from http://www.rcaap.pt/detail.jsp?id=oai:repositorio.ul.pt:10451/23616
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Rodrigues, Inês Martins. “Estruturas combinatórias associadas aos coeficientes de Littlewood-Richardson.” 2015. Thesis, Universidade de Lisboa. Accessed January 24, 2021.
http://www.rcaap.pt/detail.jsp?id=oai:repositorio.ul.pt:10451/23616.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Rodrigues, Inês Martins. “Estruturas combinatórias associadas aos coeficientes de Littlewood-Richardson.” 2015. Web. 24 Jan 2021.
Vancouver:
Rodrigues IM. Estruturas combinatórias associadas aos coeficientes de Littlewood-Richardson. [Internet] [Thesis]. Universidade de Lisboa; 2015. [cited 2021 Jan 24].
Available from: http://www.rcaap.pt/detail.jsp?id=oai:repositorio.ul.pt:10451/23616.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Rodrigues IM. Estruturas combinatórias associadas aos coeficientes de Littlewood-Richardson. [Thesis]. Universidade de Lisboa; 2015. Available from: http://www.rcaap.pt/detail.jsp?id=oai:repositorio.ul.pt:10451/23616
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Brno University of Technology
11.
Krchová, Lenka.
Symetrická grupa, její reprezentace a aplikace v molekulární a kvantové chemii: Symmetric group, its representation and applications in molecular and quantum chemistry.
Degree: 2020, Brno University of Technology
URL: http://hdl.handle.net/11012/194827
► The subject of this bachelor thesis is the study of the symmetric groups, their representation and application in molecular chemistry. At first, the particular terms…
(more)
▼ The
subject of this bachelor thesis is the study of the symmetric groups, their representation and application in molecular chemistry. At first, the particular terms from the algebra are defined, which are which are necessary to define the concept of a group. Many of them are suúpplemented by pictures for clarity and better understanding. Then, the algebraic structures, which are accompanied by clear schemes and concrete examples, are explained. Also, the symmetric groups are demonstrated on the example of the square and triangle. After that, the reader gets into the chapter about the representation of final groups where the structure of the work is similar. First, the relevant terms are defined and then the author focuses on
Young's diagrams. These are meticulůously described, few examples are mentioned and so is their working procedure. The last part of the bachelor thesis is dedicated to the operators in quantum chemistry, their principles and functions for two and three particles. This too is accompanied by examples.
Advisors/Committee Members: Kureš, Miroslav (advisor), Tomáš, Jiří (referee).
Subjects/Keywords: Grupa; symetrická grupa; reprezentace grup; Youngovy tabulky; operátory; symetrizátor; antisymetrizátor; Group; symmetric group; representation of group; Young´s tableaux; operators; symetrizator; antisymetrizator
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APA ·
Chicago ·
MLA ·
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CSE |
Export
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Manager
APA (6th Edition):
Krchová, L. (2020). Symetrická grupa, její reprezentace a aplikace v molekulární a kvantové chemii: Symmetric group, its representation and applications in molecular and quantum chemistry. (Thesis). Brno University of Technology. Retrieved from http://hdl.handle.net/11012/194827
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Krchová, Lenka. “Symetrická grupa, její reprezentace a aplikace v molekulární a kvantové chemii: Symmetric group, its representation and applications in molecular and quantum chemistry.” 2020. Thesis, Brno University of Technology. Accessed January 24, 2021.
http://hdl.handle.net/11012/194827.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Krchová, Lenka. “Symetrická grupa, její reprezentace a aplikace v molekulární a kvantové chemii: Symmetric group, its representation and applications in molecular and quantum chemistry.” 2020. Web. 24 Jan 2021.
Vancouver:
Krchová L. Symetrická grupa, její reprezentace a aplikace v molekulární a kvantové chemii: Symmetric group, its representation and applications in molecular and quantum chemistry. [Internet] [Thesis]. Brno University of Technology; 2020. [cited 2021 Jan 24].
Available from: http://hdl.handle.net/11012/194827.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Krchová L. Symetrická grupa, její reprezentace a aplikace v molekulární a kvantové chemii: Symmetric group, its representation and applications in molecular and quantum chemistry. [Thesis]. Brno University of Technology; 2020. Available from: http://hdl.handle.net/11012/194827
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
12.
Sun, Wangru.
Modèle de forêts enracinées sur des cycles et modèle de perles via les dimères : Cycle-rooted-spanning-forest model and bead model via dimers.
Degree: Docteur es, Mathématiques, 2018, Sorbonne université
URL: http://www.theses.fr/2018SORUS007
► Le modèle de dimères, également connu sous le nom de modèle de couplage parfait, est un modèle probabiliste introduit à l'origine dans la mécanique statistique.…
(more)
▼ Le modèle de dimères, également connu sous le nom de modèle de couplage parfait, est un modèle probabiliste introduit à l'origine dans la mécanique statistique. Une configuration de dimères d'un graphe est un sous-ensemble des arêtes tel que chaque sommet est incident à exactement une arête. Un poids est attribué à chaque arête et la probabilité d'une configuration est proportionnelle au produit des poids des arêtes présentes. Dans cette thèse, nous étudions principalement deux modèles qui sont liés au modèle de dimères, et plus particulièrement leur comportements limites. Le premier est le modèle des forêts couvrantes enracinées sur des cycles (CRSF) sur le tore, qui sont en bijection avec les configurations de dimères via la bijection de Temperley. Dans la limite quand la taille du tore tend vers l'infini, la mesure sur les CRSF converge vers une mesure de Gibbs ergodique sur le plan tout entier. Nous étudions la connectivité de l'objet limite, prouvons qu'elle est déterminée par le changement de hauteur moyen de la mesure de Gibbs ergodique et donnons un diagramme de phase. Le second est le modèle de perles, un processus ponctuel sur Z x R qui peut être considéré comme une limite à l'échelle du modèle de dimères sur un réseau hexagonal. Nous formulons et prouvons un principe variationnel similaire à celui du modèle dimère [CKP01], qui indique qu'à la limite de l'échelle, la fonction de hauteur normalisée d'une configuration de perles converge en probabilité vers une surface h₀ qui maximise une certaine fonctionnelle qui s'appelle "entropie". Nous prouvons également que la forme limite h₀ est une limite de l'échelle des formes limites de modèles de dimères. Il existe une correspondance entre configurations de perles et (skew) tableaux de Young standard, qui préserve la mesure uniforme sur les deux ensembles. Le principe variationnel du modèle de perles implique une forme limite d'un tableau de Young standard aléatoire. Ce résultat généralise celui de [PR09]. Nous dérivons également l'existence d'une courbe arctique d'un processus ponctuel discret qui encode les tableaux standard, défini dans [Rom12].
The dimer model, also known as the perfect matching model, is a probabilistic model originally introduced in statistical mechanics. A dimer configuration of a graph is a subset of the edges such that every vertex is incident to exactly one edge of the subset. A weight is assigned to every edge, and the probability of a configuration is proportional to the product of the weights of the edges present. In this thesis we mainly study two related models and in particular their limiting behavior. The first one is the model of cycle-rooted-spanning-forests (CRSF) on tori, which is in bijection with toroidal dimer configurations via Temperley's bijection. This gives rise to a measure on CRSF. In the limit that the size of torus tends to infinity, the CRSF measure tends to an ergodic Gibbs measure on the whole plane. We study the connectivity property of the limiting object, prove that it is determined by the average height…
Advisors/Committee Members: Tilière, Béatrice de (thesis director), Boutillier, Cédric (thesis director).
Subjects/Keywords: Modèles de dimères; Pavages; Forêts couvrantes enracinées sur cycles; Marches aléatoires; Modèle de perles; Tableaux de Young standard; Dimer model; Tilings; Cycle-rooted-spanning-forests; Random walks; Bead model; 519.2
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❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Sun, W. (2018). Modèle de forêts enracinées sur des cycles et modèle de perles via les dimères : Cycle-rooted-spanning-forest model and bead model via dimers. (Doctoral Dissertation). Sorbonne université. Retrieved from http://www.theses.fr/2018SORUS007
Chicago Manual of Style (16th Edition):
Sun, Wangru. “Modèle de forêts enracinées sur des cycles et modèle de perles via les dimères : Cycle-rooted-spanning-forest model and bead model via dimers.” 2018. Doctoral Dissertation, Sorbonne université. Accessed January 24, 2021.
http://www.theses.fr/2018SORUS007.
MLA Handbook (7th Edition):
Sun, Wangru. “Modèle de forêts enracinées sur des cycles et modèle de perles via les dimères : Cycle-rooted-spanning-forest model and bead model via dimers.” 2018. Web. 24 Jan 2021.
Vancouver:
Sun W. Modèle de forêts enracinées sur des cycles et modèle de perles via les dimères : Cycle-rooted-spanning-forest model and bead model via dimers. [Internet] [Doctoral dissertation]. Sorbonne université; 2018. [cited 2021 Jan 24].
Available from: http://www.theses.fr/2018SORUS007.
Council of Science Editors:
Sun W. Modèle de forêts enracinées sur des cycles et modèle de perles via les dimères : Cycle-rooted-spanning-forest model and bead model via dimers. [Doctoral Dissertation]. Sorbonne université; 2018. Available from: http://www.theses.fr/2018SORUS007
13.
Hage, Nohra.
Study of plactic monoids by rewriting methods : Etude des monoïdes plaxiques par des méthodes de réécriture.
Degree: Docteur es, Mathématiques, 2016, Lyon
URL: http://www.theses.fr/2016LYSES065
► Cette thèse est consacrée à l’étude des monoïdes plaxiques par une nouvelle approche utilisant des méthodes issues de la réécriture. Ces méthodes sont appliquées à…
(more)
▼ Cette thèse est consacrée à l’étude des monoïdes plaxiques par une nouvelle approche utilisant des méthodes issues de la réécriture. Ces méthodes sont appliquées à des présentations de monoïdes plaxiques décrites en termes de tableaux de Young, de bases cristallines de Kashiwara et de modèle des chemins de Littelmann. On étudie le problème des syzygies pour la présentation de Knuth des monoïdes plaxiques. En utilisant la procédure de complétion homotopique basée sur les procédures de complétion de Squier et de Knuth–Bendix, on construit des présentations cohérentes de monoïdes plaxiques de type A. Une telle présentation cohérente étend la notion de présentation convergente d’un monoïde par une famille génératrice de syzygies, décrivant toutes les relations entre les relations. On explicite une présentation cohérente finie des monoïdes plaxiques de type A avec les générateurs colonnes. Cependant, cette présentation n’est pas minimale dans le sens que plusieurs de ses générateurs sont superflus. En appliquant la procédure de réduction homotopique, on réduit cette présentation en une présentation cohérente finie qui étend la présentation de Knuth, donnantainsi toutes les syzygies des relations de Knuth. D’une manière plus générale, on étudie des présentations de monoïdes plaxiques généralisés du point de vue de la réécriture. On construit des présentations convergentes finies de ces monoïdes en utilisant les chemins de Littelmann. De plus, on étudie ces présentations pour le type C en termes de bases cristallines de Kashiwara. En introduisant les générateurs colonnes admissibles, on construit une présentation convergente finie du monoïde plaxique de type C avec des relations explicites. Cette approche nous permettrait d’étudier le problème des syzygies des présentations de monoïdes plaxiques en tout type
This thesis focuses on the study of plactic monoids by a new approach using methods issued from rewriting theory. These methods are applied on presentations of plactic monoids given in terms of Young tableaux, Kashiwara’s crystal bases and Littelmann path model. We study the syzygy problem for the Knuth presentation of the plactic monoids. Using the homotopical completion procedure that extends Squier’s and Knuth–Bendix’s completions procedure, we construct coherent presentations of plactic monoids of type A. Such a coherent presentation extends the notion of a presentation of a monoid by a family of generating syzygies, taking into account all the relations among the relations. We make explicit a finite coherent presentation of plactic monoids of type A with the column generators. However, this presentation is not minimal in the sense that many of its generators are superfluous. After applying the homotopical reduction procedure on this presentation, we reduce it to a finite coherent one that extends the Knuth presentation, giving then all the syzygies of the Knuth relations. More generally, we deal with presentations of plactic monoids of any type from the rewriting theory perspective. We construct finite…
Advisors/Committee Members: Gaussent, Stéphane (thesis director), Malbos, Philippe (thesis director).
Subjects/Keywords: Monoïdes plaxiques; Réécriture; Problème du mot; Problème des syzygies; Présentations convergentes; Présentations cohérentes; Complétion de Squier; Complétion de Knuth–Bendix; Tableaux de Young; Algorithmes d’insertion de Schensted; Algorithmes d’insertion de Lecouvey; Bases cristallines; Modèle des chemins de Littelmann; Plactic monoids; Rewriting theory; Word problem; Syzygies problem; Convergent presentations; Coherent presentations; Squier’s completion; Knuth–Bendix’s completion; Young tableaux; Schensted’s insertion algorithm; Lecouvey’s insetion algorithm; Crystal bases; Littelmann path model
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❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Hage, N. (2016). Study of plactic monoids by rewriting methods : Etude des monoïdes plaxiques par des méthodes de réécriture. (Doctoral Dissertation). Lyon. Retrieved from http://www.theses.fr/2016LYSES065
Chicago Manual of Style (16th Edition):
Hage, Nohra. “Study of plactic monoids by rewriting methods : Etude des monoïdes plaxiques par des méthodes de réécriture.” 2016. Doctoral Dissertation, Lyon. Accessed January 24, 2021.
http://www.theses.fr/2016LYSES065.
MLA Handbook (7th Edition):
Hage, Nohra. “Study of plactic monoids by rewriting methods : Etude des monoïdes plaxiques par des méthodes de réécriture.” 2016. Web. 24 Jan 2021.
Vancouver:
Hage N. Study of plactic monoids by rewriting methods : Etude des monoïdes plaxiques par des méthodes de réécriture. [Internet] [Doctoral dissertation]. Lyon; 2016. [cited 2021 Jan 24].
Available from: http://www.theses.fr/2016LYSES065.
Council of Science Editors:
Hage N. Study of plactic monoids by rewriting methods : Etude des monoïdes plaxiques par des méthodes de réécriture. [Doctoral Dissertation]. Lyon; 2016. Available from: http://www.theses.fr/2016LYSES065

Georgia Tech
14.
Litherland, Trevis J.
On the limiting shape of random young tableaux for Markovian words.
Degree: PhD, Mathematics, 2008, Georgia Tech
URL: http://hdl.handle.net/1853/26607
► The limiting law of the length of the longest increasing subsequence, LI_n, for sequences (words) of length n arising from iid letters drawn from finite,…
(more)
▼ The limiting law of the length of the longest increasing subsequence, LI_n, for sequences (words) of length n arising from iid letters drawn from finite, ordered alphabets is studied using a straightforward Brownian functional approach. Building on the insights gained in both the uniform and non-uniform iid cases, this approach is then applied to iid countable alphabets. Some partial results associated with the extension to independent, growing alphabets are also given. Returning again to the finite setting, and keeping with the same Brownian formalism, a generalization is then made to words arising from irreducible, aperiodic, time-homogeneous Markov chains on a finite, ordered alphabet. At the same time, the probabilistic object, LI_n, is simultaneously generalized to the shape of the associated
Young tableau given by the well-known RSK-correspondence. Our results on this limiting shape describe, in detail, precisely when the limiting shape of the
Young tableau is (up to scaling) that of the iid case, thereby answering a conjecture of Kuperberg. These results are based heavily on an analysis of the covariance structure of an m-dimensional Brownian motion and the precise form of the Brownian functionals. Finally, in both the iid and more general Markovian cases, connections to the limiting laws of the spectrum of certain random matrices associated with the Gaussian Unitary Ensemble (GUE) are explored.
Advisors/Committee Members: Houdre, Christian (Committee Chair), Bakhtin, Yuri (Committee Member), Foley, Robert (Committee Member), Koltchinskii, Vladimir (Committee Member), Lifshitz, Mikhail (Committee Member), Matzinger, Heinrich (Committee Member), Popescu, Ionel (Committee Member).
Subjects/Keywords: Cyclic matrices; Brownian functional; Young tableaux; Markovian words; Invariance principle; Random variables; Probabilities; Asymptotic distribution (Probability theory)
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APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Litherland, T. J. (2008). On the limiting shape of random young tableaux for Markovian words. (Doctoral Dissertation). Georgia Tech. Retrieved from http://hdl.handle.net/1853/26607
Chicago Manual of Style (16th Edition):
Litherland, Trevis J. “On the limiting shape of random young tableaux for Markovian words.” 2008. Doctoral Dissertation, Georgia Tech. Accessed January 24, 2021.
http://hdl.handle.net/1853/26607.
MLA Handbook (7th Edition):
Litherland, Trevis J. “On the limiting shape of random young tableaux for Markovian words.” 2008. Web. 24 Jan 2021.
Vancouver:
Litherland TJ. On the limiting shape of random young tableaux for Markovian words. [Internet] [Doctoral dissertation]. Georgia Tech; 2008. [cited 2021 Jan 24].
Available from: http://hdl.handle.net/1853/26607.
Council of Science Editors:
Litherland TJ. On the limiting shape of random young tableaux for Markovian words. [Doctoral Dissertation]. Georgia Tech; 2008. Available from: http://hdl.handle.net/1853/26607

University of Central Florida
15.
Katona, Gregory.
Field Theoretic Lagrangian From Off-shell Supermultiplet Gauge Quotients.
Degree: 2013, University of Central Florida
URL: https://stars.library.ucf.edu/etd/4469
► Recent efforts to classify off-shell representations of supersymmetry without a central charge have focused upon directed, supermultiplet graphs of hypercubic topology known as Adinkras.…
(more)
▼ Recent efforts to classify off-shell representations of supersymmetry without a central charge have focused upon directed, supermultiplet graphs of hypercubic topology known as Adinkras. These encodings of Super Poincare algebras, depict every generator of a chosen supersymmetry as a node-pair transformtion between fermionic bosonic component fields. This research thesis is a culmination of investigating novel diagrammatic sums of gauge-quotients by supersymmetric images of other Adinkras, and the correlated building of field theoretic worldline Lagrangians to accommodate both classical and quantum venues. We find Ref [40], that such gauge quotients do not yield other stand alone or "proper" Adinkras as afore sighted, nor can they be decomposed into supermultiplet sums, but are rather a connected "Adinkraic network". Their iteration, analogous to Weyl's construction for producing all finite-dimensional unitary representations in Lie algebras, sets off chains of algebraic paradigms in discrete-graph and continuous-field variables, the links of which feature distinct, supersymmetric Lagrangian templates. Collectively, these Adiankraic series air new symbolic genera for equation to phase moments in Feynman path integrals. Guided in this light, we proceed by constructing Lagrangians actions for the N = 3 supermultiplet YI /(iDI X) for I = 1, 2, 3, where YI and X are standard, Salam-Strathdee superfields: YI fermionic and X bosonic. The system, bilinear in the component fields exhibits a total of thirteen free parameters, seven of which specify Zeeman-like coupling to external background (magnetic) fluxes. All but special subsets of this parameter space describe aperiodic oscillatory responses, some of which are found to be surprisingly controlled by the golden ratio, [phi] = 1.61803, Ref [52]. It is further determined that these Lagrangians allow an N = 3 -> 4 supersymmetric extension to the Chiral-Chiral and Chiral-twistedChiral multiplet, while a subset admits two inequivalent such extensions. In a natural proiii gression, a continuum of observably and usefully inequivalent, finite-dimensional off-shell representations of worldline N = 4 extended supersymmetry are explored, that are variate from one another but in the value of a tuning parameter, Ref [53]. Their dynamics turns out to be nontrivial already when restricting to just bilinear Lagrangians. In particular, we find a 34-parameter family of bilinear Lagrangians that couple two differently tuned supermultiplets to each other and to external magnetic fluxes, where the explicit parameter dependence is unremovable by any field redefinition and is therefore observable. This offers the evaluation of X-phase sensitive, off-shell path integrals with promising correlations to group product decompositions and to deriving source emergences of higher-order background flux-forms on 2-dimensional manifolds, the stacks of which comprise space-time volumes. Application to nonlinear sigma models would naturally follow, having potential use in M- and F- string theories.
Advisors/Committee Members: Klemm, Richard.
Subjects/Keywords: Supersymmetry; superspace; supermultiplet; adinkra; automata; adiankraic tensor product decomposition; group theoretic; lorentz group; su(2); so(3); gauge quotient; isomorphism; surjective; bijective; image mapping; indefinite adiankraic network sequence; super poincare group; haag lopuszanski sohnius theorem; string theory; m theory; f theory; nonlinear sigma model; (numerical) algebraic geometry; algebraic paradigms; worldsheet; worldsheet stacks; supersymmetric lagrangians; ansatz templates; super potentials; quantum mechanics; field theory; fermionic; bosonic; (super) zeeman; background flux fields; supergravity; superfields; young tableaux; susy tableaux; controlled chaos; supercharge continuum; chiral; chiral twisted chiral; Physics
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APA (6th Edition):
Katona, G. (2013). Field Theoretic Lagrangian From Off-shell Supermultiplet Gauge Quotients. (Doctoral Dissertation). University of Central Florida. Retrieved from https://stars.library.ucf.edu/etd/4469
Chicago Manual of Style (16th Edition):
Katona, Gregory. “Field Theoretic Lagrangian From Off-shell Supermultiplet Gauge Quotients.” 2013. Doctoral Dissertation, University of Central Florida. Accessed January 24, 2021.
https://stars.library.ucf.edu/etd/4469.
MLA Handbook (7th Edition):
Katona, Gregory. “Field Theoretic Lagrangian From Off-shell Supermultiplet Gauge Quotients.” 2013. Web. 24 Jan 2021.
Vancouver:
Katona G. Field Theoretic Lagrangian From Off-shell Supermultiplet Gauge Quotients. [Internet] [Doctoral dissertation]. University of Central Florida; 2013. [cited 2021 Jan 24].
Available from: https://stars.library.ucf.edu/etd/4469.
Council of Science Editors:
Katona G. Field Theoretic Lagrangian From Off-shell Supermultiplet Gauge Quotients. [Doctoral Dissertation]. University of Central Florida; 2013. Available from: https://stars.library.ucf.edu/etd/4469
.