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Hecke algebra deformations of Coxter group actions

Algebra & Discrete Mathematics

Speaker: Monica Vazirani, UC Davis
Location: 2112 MSB
Start time: Fri, Oct 7 2011, 2:10PM

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 on cosets W/U. Our motivating example is the action of the symmetric group on fixed-point-free involutions by conjugation. 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. This is joint work with Eric Rains.