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You searched for subject:(classical invariant theory). Showing records 1 – 3 of 3 total matches.

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1. Olive, Marc. Géométrie des espaces de tenseurs : une approche effective appliquée à la mécanique des milieux continus : Geometry of tensor spaces : an effective approach applied to continuum mechanics.

Degree: Docteur es, Mathématiques, 2014, Aix Marseille Université

Plusieurs lois de comportement mécaniques possèdent une formulation tensorielle, comme c'est le cas pour l'élasticité où intervient un espace de tenseurs d'ordre 4, noté Ela. La classification des matériaux élastiques passent par la nécessité de décrire l'espace des orbites ELA/SO(3). Plus généralement, on étudie la géométrie d'un espace de tenseurs sur ℝ3, via l'action du groupe O(3). Cette géométrie est caractérisée par ses classes d'isotropies, ou encore classes de symétries. Tout espace de tenseurs possède en effet un nombre fini de classes d'isotropies. Nous proposons alors une méthode originale et générale pour obtenir ces classes d'istropie. Nous avons ainsi pu obtenir pour la première fois les classes d'isotropie d'un espace de tenseurs d'ordre 8 intervenant en théorie de l'élasticité linéaire du second-gradient de la déformation.Pour une représentation réelle d'un groupe compact, l'algèbre des polynômes invariants sépare les orbites, d'où la recherche d'une famille génératrice minimale de cette algèbre. Pour cela, on exploitant le lien entre les espaces de tenseurs et les espaces de formes binaires. Nous avons ainsi repris et ré-interprété les approches effectives de cette théorie, développées par Gordan au 19ième siècle. Cette ré-interprétation nous a permis d'obtenir de nombreux résultats, dont une famille génératrice minimale d'invariants pour l'élasticité mais aussi pour la piézoélectricté. Nous avons pu retrouver d'une façon simple les séries de Gordan, ainsi que des relations plus récentes d'Abdesselam – Chipalkatti sur les transvectants de formes binaires.

Tensorial formulation of mechanical constitutive equations is a very important matter in continuum mechanics. For instance, the space of elastic tensors is a subspace of 4th order tensors with a natural SO(3) group action. More generaly, we have to study the geometry of a tensor space defined on ℝ3, under O(3) group action.To describe such a geometry, we first have to exhibit its isotropy classes, also named symetry classes. Indeed, each tensor space possesses a finite number of isotropy classes. In this present work, we propose an original method to obtain isotropy classes of a given tensor space. As an illustration of this new method, we get for the first time the isotropy classes of a 8th order tensor space occuring in second strain-gradient elasticity theory. In the case of a real representation of a compact group, invariant algebra seperates the orbits. This observation motivates the purpose to find a finite generating set of polynomial invariants. For that purpose, we make use of the link between tensor spaces and spaces of binary forms, which belongs to the classical invariant theory. We thus have to deal with SL(2,ℂ) group action. To obtain new results, we have reformulated and reinterpreted effective approaches of Gordan's algorithm, developped during XIXth century. We then obtain for the first time a minimal generating family of elasticity tensor space, and a generating family of piezoelectricity…

Advisors/Committee Members: Kolev, Boris (thesis director), Auffray, Nicolas (thesis director).

Subjects/Keywords: Théorie classique des invariants; Transvectants; Covariants de formes binaires; Elasticité linéaire; Classical invariant theory; Transvectants; Covariants of binary forms; Linear elasticity

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APA (6th Edition):

Olive, M. (2014). Géométrie des espaces de tenseurs : une approche effective appliquée à la mécanique des milieux continus : Geometry of tensor spaces : an effective approach applied to continuum mechanics. (Doctoral Dissertation). Aix Marseille Université. Retrieved from http://www.theses.fr/2014AIXM4745

Chicago Manual of Style (16th Edition):

Olive, Marc. “Géométrie des espaces de tenseurs : une approche effective appliquée à la mécanique des milieux continus : Geometry of tensor spaces : an effective approach applied to continuum mechanics.” 2014. Doctoral Dissertation, Aix Marseille Université. Accessed August 05, 2020. http://www.theses.fr/2014AIXM4745.

MLA Handbook (7th Edition):

Olive, Marc. “Géométrie des espaces de tenseurs : une approche effective appliquée à la mécanique des milieux continus : Geometry of tensor spaces : an effective approach applied to continuum mechanics.” 2014. Web. 05 Aug 2020.

Vancouver:

Olive M. Géométrie des espaces de tenseurs : une approche effective appliquée à la mécanique des milieux continus : Geometry of tensor spaces : an effective approach applied to continuum mechanics. [Internet] [Doctoral dissertation]. Aix Marseille Université 2014. [cited 2020 Aug 05]. Available from: http://www.theses.fr/2014AIXM4745.

Council of Science Editors:

Olive M. Géométrie des espaces de tenseurs : une approche effective appliquée à la mécanique des milieux continus : Geometry of tensor spaces : an effective approach applied to continuum mechanics. [Doctoral Dissertation]. Aix Marseille Université 2014. Available from: http://www.theses.fr/2014AIXM4745

2. MA JIAJUN. Two Topics on Local Theta Correspondence.

Degree: 2012, National University of Singapore

Subjects/Keywords: Representation theory of classical groups; local theta correspondence; invariant theory; transfer of K-type; associated cycle; highest weight module

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

JIAJUN, M. (2012). Two Topics on Local Theta Correspondence. (Thesis). National University of Singapore. Retrieved from http://scholarbank.nus.edu.sg/handle/10635/36425

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):

JIAJUN, MA. “Two Topics on Local Theta Correspondence.” 2012. Thesis, National University of Singapore. Accessed August 05, 2020. http://scholarbank.nus.edu.sg/handle/10635/36425.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

JIAJUN, MA. “Two Topics on Local Theta Correspondence.” 2012. Web. 05 Aug 2020.

Vancouver:

JIAJUN M. Two Topics on Local Theta Correspondence. [Internet] [Thesis]. National University of Singapore; 2012. [cited 2020 Aug 05]. Available from: http://scholarbank.nus.edu.sg/handle/10635/36425.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

JIAJUN M. Two Topics on Local Theta Correspondence. [Thesis]. National University of Singapore; 2012. Available from: http://scholarbank.nus.edu.sg/handle/10635/36425

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

3. Im, Mee Seong. On semi-invariants of filtered representations of quivers and the cotangent bundle of the enhanced Grothendieck-Springer resolution.

Degree: PhD, 0439, 2014, University of Illinois – Urbana-Champaign

We introduce the notion of filtered representations of quivers, which is related to usual quiver representations, but is a systematic generalization of conjugacy classes of n ×  n matrices to (block) upper triangular matrices up to conjugation by invertible (block) upper triangular matrices. With this notion in mind, we describe the ring of invariant polynomials for interesting families of quivers, namely, finite ADE-Dynkin quivers and affine type \widetilde{A}-Dynkin quivers. We then study their relation to an important and fundamental object in representation theory called the Grothendieck-Springer resolution, and we conclude by stating several conjectures, suggesting further research. Advisors/Committee Members: Nevins, Thomas A. (advisor), Kedem, Rinat (Committee Chair), Nevins, Thomas A. (committee member), Bergvelt, Maarten J. (committee member), Schenck, Henry K. (committee member).

Subjects/Keywords: Algebraic geometry; representation theory; quiver varieties; filtered quiver variety; quiver flag variety; semi-invariant polynomials; invariant subring; Derksen-Weyman; Domokos-Zubkov; Schofield-van den Bergh; ADE-Dynkin quivers; affine Dynkin quivers; quivers with at most two pathways between any two vertices; filtration of vector spaces; classical invariant theory; the Hamiltonian reduction of the cotangent bundle of the enhanced Grothendieck-Springer resolution; almost-commuting varieties; affine quotient

…This amounts to a generalization of classical problems of invariant theory to this new… …triangular change of basis. Next, we introduce some definitions from invariant theory. Let χ : G… …invariant theory of semisimple or reductive groups and do not apply in the filtered situation. As… …invariant polynomials for acyclic quivers by using representation theory techniques, and in 2001… …x5D;, which coincides with the classical result that generators of the ring of invariant… 

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Im, M. S. (2014). On semi-invariants of filtered representations of quivers and the cotangent bundle of the enhanced Grothendieck-Springer resolution. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/49392

Chicago Manual of Style (16th Edition):

Im, Mee Seong. “On semi-invariants of filtered representations of quivers and the cotangent bundle of the enhanced Grothendieck-Springer resolution.” 2014. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed August 05, 2020. http://hdl.handle.net/2142/49392.

MLA Handbook (7th Edition):

Im, Mee Seong. “On semi-invariants of filtered representations of quivers and the cotangent bundle of the enhanced Grothendieck-Springer resolution.” 2014. Web. 05 Aug 2020.

Vancouver:

Im MS. On semi-invariants of filtered representations of quivers and the cotangent bundle of the enhanced Grothendieck-Springer resolution. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2014. [cited 2020 Aug 05]. Available from: http://hdl.handle.net/2142/49392.

Council of Science Editors:

Im MS. On semi-invariants of filtered representations of quivers and the cotangent bundle of the enhanced Grothendieck-Springer resolution. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2014. Available from: http://hdl.handle.net/2142/49392

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