Generic Algebras and Kazhdan-Lusztig Theory for Monomial Groups

• Main Author: Alhaddad, Shemsi I.
• Other Authors: Douglass, Matthew
• Format: Others
• Language: English
• Published: University of North Texas 2006
• Subjects: Hecke algebras.; Kazhdan-Lusztig polynomials.; Coxeter groups.; Hecke algebra; Kazhdan-Lusztig theory; monomial groups
• Online Access: https://digital.library.unt.edu/ark:/67531/metadc5235/

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.