Generic Hecke Algebras for Monomial Groups

Details Generic Hecke Algebras for Monomial Groups Generic Hecke Algebras for Monomial Groups

2006-10-05

arxiv.org/abs/math/0610159v3

Mathematics

Representation Theory

25 pages; This is a substantive revision. A construction of a Kazhdan-Lusztig C basis and Kazhdan-Lusztig polynomials for H wa

Scientific paper

In this paper we define a two-variable, generic Hecke algebra, H, for each complex reflection group G(b,1,n). The algebra H specializes to the group algebra of G(b,1,n) and also to an endomorphism algebra of a representation of GL(n,q) induced from a solvable subgroup. We construct Kazhdan-Lusztig "R-polynomials" for H and show that they may be used to define a partial order on G(b,1,n). Using a generalization of Deodhar's notion of distinguished subexpressions we give a closed formula for the R-polynomials. After passing to a one-variable quotient of the ring of scalars, we construct Kazhdan-Lusztig polynomials for H that reduce to the usual Kazhdan-Lusztig polynomials for the symmetric group when b=1.

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