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.
| Identifer | oai:union.ndltd.org:unt.edu/info:ark/67531/metadc5235 |
| Date | 05 1900 |
| Creators | Alhaddad, Shemsi I. |
| Contributors | Douglass, Matthew, Bator, Elizabeth M., Brozovic, Douglas, Shepler, Anne, Thiem, Nathanial |
| Publisher | University of North Texas |
| Source Sets | University of North Texas |
| Language | English |
| Detected Language | English |
| Type | Thesis or Dissertation |
| Format | Text |
| Rights | Use restricted to UNT Community, Copyright, Alhaddad, Shemsi I., Copyright is held by the author, unless otherwise noted. All rights reserved. |
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