Generic Algebras and Kazhdan-Lusztig Theory for Monomial Groups

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Description:

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.

Creator(s): Alhaddad, Shemsi I.
Creation Date: May 2006
Partner(s):
UNT Libraries
Collection(s):
UNT Theses and Dissertations
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Publisher Info:
Publisher Name: University of North Texas
Place of Publication: Denton, Texas
Date(s):
  • Creation: May 2006
  • Digitized: April 22, 2008
Description:

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.

Degree:
Level: Doctoral
Discipline: Mathematics
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Subject(s):
Keyword(s): Hecke algebra | Kazhdan-Lusztig theory | monomial groups
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Partner:
UNT Libraries
Collection:
UNT Theses and Dissertations
Identifier:
  • OCLC: 70279569 |
  • ARK: ark:/67531/metadc5235
Resource Type: Thesis or Dissertation
Format: Text
Rights:
Access: Use restricted to UNT Community
License: Copyright
Holder: Alhaddad, Shemsi I.
Statement: Copyright is held by the author, unless otherwise noted. All rights reserved.