# Coxeter groups and palindromic Poincare polynomials

SPEAKER: Edward Richmond

TITLE: Coxeter groups and palindromic Poincare polynomials

ABSTRACT: Let W be a Coxeter group. For any w in W, let P_w denote the Poincare polynomial of w (i.e. the generating function of the principle order ideal of w with respect to length). If W is the Weyl group of some Kac-Moody group G, then P_w is the usual Poincare polynomial of the corresponding Schubert varitey X_w. In this talk, I will discuss work in progress with W. Slofstra on detecting when the sequence of coefficients of a Poincare polynomial are the same read forwards and backwards (i.e. palindromic). The polynomial P_w satisfies this property precisely when the Schubert variety X_w is rationally smooth. It turns out that for many Coxeter groups, this property is relatively easy to detect.