Research
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Education: PhD, Mathematics, University of North Texas, May 2006

Thesis Title
:  "Generic Algebras and Kazhdan-Lusztig Theory for Monomial Groups."

Thesis Abstract
:
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.

Statement of Research Interests (PDF)

Preprints:  "Generic Hecke Algebras for Monomial Groups"  http://arxiv.org/abs/math.RT/0610159


Last updated September 2, 2007