EVENT DETAILS AND ABSTRACT

Title: Coxeter representations appearing in the cohomology of hyperplane complements
Speaker: Joel Specter
Speaker Info: Northwestern University
Brief Description:
Special Note:
Abstract:

Given a finite Coxeter group W, there exists a unique irreducible, real representation V of W on which W acts as a reflection group. Let X(W) be the complement of the reflection hyperplanes in the complexification of V. Deligne showed that X(W) is a classifying space for the pure Artin-tits group attached to W. In this talk, I will expand on work of Arnol'd, Brieskorn, Orlick and Solomon, and Lehrer to give an explicit formula for the character of the $W$ on the cohomology of $X(W)$. The proof will use etale cohomology to equate this calculation to a counting problem in elementary number theory over finite fields. This is joint work with Weiyan Chen.