Generic Algebras and Kazhdan-Lusztig Theory for Monomial Groups

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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.

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Alhaddad, Shemsi I. May 2006.

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  • Alhaddad, Shemsi I.

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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.

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  • May 2006

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  • May 5, 2008, 2:14 p.m.

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  • Jan. 14, 2014, 12:23 p.m.

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Alhaddad, Shemsi I. Generic Algebras and Kazhdan-Lusztig Theory for Monomial Groups, dissertation, May 2006; Denton, Texas. (digital.library.unt.edu/ark:/67531/metadc5235/: accessed June 23, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .