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

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1. Gedeon, Katie. Kazhdan-Lusztig Polynomials of Matroids and Their Roots.

Degree: PhD, Department of Mathematics, 2018, University of Oregon

The Kazhdan-Lusztig polynomial of a matroid M, denoted PM( t ), was recently defined by Elias, Proudfoot, and Wakefield. These polynomials are analogous to the classical Kazhdan-Lusztig polynomials associated with Coxeter groups. For example, in both cases there is a purely combinatorial recursive definition. Furthermore, in the classical setting, if the Coxeter group is a Weyl group then the Kazhdan-Lusztig polynomial is a Poincare polynomial for the intersection cohomology of a particular variety; in the matroid setting, if M is a realizable matroid then the Kazhdan-Lusztig polynomial is also the intersection cohomology Poincare polynomial of a variety corresponding to M. (Though there are several analogies between the two types of polynomials, the theory is quite different.) Here we compute the Kazhdan-Lusztig polynomials of several graphical matroids, including thagomizer graphs, the complete bipartite graph K2,n, and (conjecturally) fan graphs. Additionally, we investigate a conjecture by the author, Proudfoot, and Young on the real-rootedness for Kazhdan-Lusztig polynomials of these matroids as well as a conjecture on the interlacing behavior of these roots. We also show that the Kazhdan-Lusztig polynomials of uniform matroids of rank n − 1 on n elements are real-rooted. This dissertation includes both previously published and unpublished co-authored material. Advisors/Committee Members: Proudfoot, Nicholas (advisor).

Subjects/Keywords: Kazhdan-Lusztig polynomials; Matroid theory; real-rootedness

…laid out the analogy between this new theory and the classical theory of Kazhdan-Lusztig… …Matroids and Their Kazhdan-Lusztig Polynomials . . . . . . . 5 2.2. Equivariant Matroids and… …The Equivariant Kazhdan-Lusztig Polynomial… …30 ROOTS OF KAZHDAN-LUSZTIG POLYNOMIALS OF MATROIDS… …xii LIST OF TABLES Table Page 4.1. Kazhdan-Lusztig polynomials of some uniform matroids… 

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APA (6th Edition):

Gedeon, K. (2018). Kazhdan-Lusztig Polynomials of Matroids and Their Roots. (Doctoral Dissertation). University of Oregon. Retrieved from http://hdl.handle.net/1794/23913

Chicago Manual of Style (16th Edition):

Gedeon, Katie. “Kazhdan-Lusztig Polynomials of Matroids and Their Roots.” 2018. Doctoral Dissertation, University of Oregon. Accessed December 05, 2020. http://hdl.handle.net/1794/23913.

MLA Handbook (7th Edition):

Gedeon, Katie. “Kazhdan-Lusztig Polynomials of Matroids and Their Roots.” 2018. Web. 05 Dec 2020.

Vancouver:

Gedeon K. Kazhdan-Lusztig Polynomials of Matroids and Their Roots. [Internet] [Doctoral dissertation]. University of Oregon; 2018. [cited 2020 Dec 05]. Available from: http://hdl.handle.net/1794/23913.

Council of Science Editors:

Gedeon K. Kazhdan-Lusztig Polynomials of Matroids and Their Roots. [Doctoral Dissertation]. University of Oregon; 2018. Available from: http://hdl.handle.net/1794/23913


University of North Texas

2. Alhaddad, Shemsi I. Generic Algebras and Kazhdan-Lusztig Theory for Monomial Groups.

Degree: 2006, University of North Texas

The Iwahori-Hecke algebras of Coxeter groups play a central role in the study of representations of semisimple Lie-type groups. An important tool is the combinatorial approach to representations of Iwahori-Hecke algebras introduced by Kazhdan and Lusztig in 1979. In this dissertation, I discuss a generalization of the Iwahori-Hecke algebra of the symmetric group that is instead based on the complex reflection group G(r,1,n). Using the analogues of Kazhdan and Lusztig's R-polynomials, I show that this algebra determines a partial order on G(r,1,n) that generalizes the Chevalley-Bruhat order on the symmetric group. I also consider possible analogues of Kazhdan-Lusztig polynomials. Advisors/Committee Members: Douglass, Matthew, Bator, Elizabeth M., Brozovic, Douglas, Shepler, Anne, Thiem, Nathanial.

Subjects/Keywords: Hecke algebras.; Kazhdan-Lusztig polynomials.; Coxeter groups.; Hecke algebra; Kazhdan-Lusztig theory; monomial groups

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APA (6th Edition):

Alhaddad, S. I. (2006). Generic Algebras and Kazhdan-Lusztig Theory for Monomial Groups. (Thesis). University of North Texas. Retrieved from https://digital.library.unt.edu/ark:/67531/metadc5235/

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):

Alhaddad, Shemsi I. “Generic Algebras and Kazhdan-Lusztig Theory for Monomial Groups.” 2006. Thesis, University of North Texas. Accessed December 05, 2020. https://digital.library.unt.edu/ark:/67531/metadc5235/.

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

MLA Handbook (7th Edition):

Alhaddad, Shemsi I. “Generic Algebras and Kazhdan-Lusztig Theory for Monomial Groups.” 2006. Web. 05 Dec 2020.

Vancouver:

Alhaddad SI. Generic Algebras and Kazhdan-Lusztig Theory for Monomial Groups. [Internet] [Thesis]. University of North Texas; 2006. [cited 2020 Dec 05]. Available from: https://digital.library.unt.edu/ark:/67531/metadc5235/.

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

Council of Science Editors:

Alhaddad SI. Generic Algebras and Kazhdan-Lusztig Theory for Monomial Groups. [Thesis]. University of North Texas; 2006. Available from: https://digital.library.unt.edu/ark:/67531/metadc5235/

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

3. Xu, Tianyuan. On the Subregular J-ring of Coxeter Systems.

Degree: PhD, Department of Mathematics, 2017, University of Oregon

Let (W, S) be an arbitrary Coxeter system, and let J be the asymptotic Hecke algebra associated to (W, S) via Kazhdan-Lusztig polynomials by Lusztig. We study a subalgebra J_C of J corresponding to the subregular cell C of W . We prove a factorization theorem that allows us to compute products in J_C without inputs from Kazhdan-Lusztig theory, then discuss two applications of this result. First, we describe J_C in terms of the Coxeter diagram of (W, S) in the case (W, S) is simply- laced, and deduce more connections between the diagram and J_C in some other cases. Second, we prove that for certain specific Coxeter systems, some subalgebras of J_C are free fusion rings, thereby connecting the algebras to compact quantum groups arising in operator algebra theory. Advisors/Committee Members: Ostrik, Victor (advisor).

Subjects/Keywords: Coxeter groups; Fusion categories; Hecke algebras; Kazhdan-Lusztig theory; Partition quantum groups; Tensor categories

…8 8 12 15 17 III. HECKE ALGEBRAS 25 3.1. Hecke Algebras and Their Kazhdan-Lusztig Bases… …25 3.2. Kazhdan-Lusztig Cells . . . . . . . . . . . . . . . . . . . . . . . . . 30 3.3. The… …Kazhdan-Lusztig polynomials, Lusztig constructed the asymptotic Hecke algebra J of (W, S… …constants of the Kazhdan-Lusztig basis of the Hecke algebra H of (W, S). The non… …Kazhdan-Lusztig cell E of W , the subgroup JE = ⊕w∈E Ztw of J is a subalgebra of J and also a… 

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

APA (6th Edition):

Xu, T. (2017). On the Subregular J-ring of Coxeter Systems. (Doctoral Dissertation). University of Oregon. Retrieved from http://hdl.handle.net/1794/22741

Chicago Manual of Style (16th Edition):

Xu, Tianyuan. “On the Subregular J-ring of Coxeter Systems.” 2017. Doctoral Dissertation, University of Oregon. Accessed December 05, 2020. http://hdl.handle.net/1794/22741.

MLA Handbook (7th Edition):

Xu, Tianyuan. “On the Subregular J-ring of Coxeter Systems.” 2017. Web. 05 Dec 2020.

Vancouver:

Xu T. On the Subregular J-ring of Coxeter Systems. [Internet] [Doctoral dissertation]. University of Oregon; 2017. [cited 2020 Dec 05]. Available from: http://hdl.handle.net/1794/22741.

Council of Science Editors:

Xu T. On the Subregular J-ring of Coxeter Systems. [Doctoral Dissertation]. University of Oregon; 2017. Available from: http://hdl.handle.net/1794/22741

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