CU Algebraic Lie Theory Seminar

Homology representations of Coxeter groups

Richard Green, CU

October 7
2-3pm
Math 220

Abstract

Many finite Coxeter groups occur naturally as groups of automorphisms of polytopes (higher dimensional polyhedra). Some of my recent work considers subcomplexes of these polytopes, that is, spaces obtained by deleting interiors of certain faces. If these subcomplexes are chosen carefully, their homology groups (don't worry, I'll explain this) afford representations of the Coxeter group. I will discuss how one might find the characters of such representations, concentrating mostly on the case of type D. This will be a good excuse to discuss the representation theory of finite Coxeter groups of classical type (A, B, D) over the complex numbers.