Generic Hecke Algebras for Monomial Groups
摘要
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.
引用
@article{arxiv.math/0610159,
title = {Generic Hecke Algebras for Monomial Groups},
author = {S. I. Alhaddad and J. M. Douglass},
journal= {arXiv preprint arXiv:math/0610159},
year = {2010}
}
备注
25 pages; This is a substantive revision. A construction of a Kazhdan-Lusztig C basis and Kazhdan-Lusztig polynomials for H was added. A lot of typos were fixed. Some new typos might have been introduced