Monica Vazirani: Deformations of permutation representations of Coxeter groups
Abstract
One can deform a Coxeter group W to its corresponding Hecke algebra H(W)
and a standard parabolic subgroup W_I to a corresponding subalgebra H(W_I).
However, this is not the case for every subgroup U, even if U is conjugate
parabolic.
Sometimes one can still deform the associated permutation representation
W/U.
In this talk, I'll define a larger class of "quasiparabolic" subgroups and
more generally quasiparabolic W-sets, and show that they admit a flat
deformation
over Z[q] to a representation of H(W). They also share other nice properties
with W/W_I such as a shellable Bruhat order.
Our motivating example is the action of the symmetric group on
fixed-point-free
involutions by conjugation.
This is joint work with Eric Rains.