Research
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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