University of Minnesota Combinatorics Seminar
Friday, February 26, 2010
3:35pm in 570 Vincent Hall



Affine descents and the Steinberg torus

Kevin Dilks

Univ. of Minnesota


Abstract

Any irreducible affine Weyl group can be written as the semi-direct product of the associated finite Weyl group, W, with the translation subgroup. The Steinberg torus is defined to be the Coxeter complex of the affine Weyl group after quotienting by the translation subgroup, and has facets in bijection with the elements of W.

In this talk, I will show how the h-vectors of both the Coxeter complex and the Steinberg torus have combinatorial interpretations as generating functions of descent-like statistics. Additionally, I will show that these polynomials have a non-negative expansion in a natural symmetric and unimodal basis (ie, are "gamma-positive") arising from peak statistics, and present a number of formulas and relations for these polynomials in the classical cases.

This is joint work with Kyle Petersen and John Stembridge.