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Generic Algebras and Kazhdan-Lusztig Theory for Monomial Groups

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.

Identiferoai:union.ndltd.org:unt.edu/info:ark/67531/metadc5235
Date05 1900
CreatorsAlhaddad, Shemsi I.
ContributorsDouglass, Matthew, Bator, Elizabeth M., Brozovic, Douglas, Shepler, Anne, Thiem, Nathanial
PublisherUniversity of North Texas
Source SetsUniversity of North Texas
LanguageEnglish
Detected LanguageEnglish
TypeThesis or Dissertation
FormatText
RightsUse restricted to UNT Community, Copyright, Alhaddad, Shemsi I., Copyright is held by the author, unless otherwise noted. All rights reserved.

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