CU Algebraic Lie Theory Seminar

CU Algebraic Lie Theory Seminar
The cohomology of hyperplane complements and Solomon's descent algebra J. Matthew Douglass, University of Northern Texas, Denton
February 22, 2011 Math 220 2-3pm	Abstract Suppose W is a finite Coxeter group. In this talk I'll explain a conjectural relation between (1) the representation of W on the cohomology of the complement of the arrangement of W and (2) the regular representation of W via the descent algebra of W. It is expected that both the group algebra of W and the cohomology of the complement can be decomposed into a sum of induced one-dimensional representations of element centralizers, one for each conjugacy class of elements of W. The conjecture is known to be true for symmetric groups, dihedral groups, and is being checked for all low rank Coxeter groups using GAP and CHEVIE. This is joint work with Gerhard Riehrle and Goetz Pfeiffer.

The cohomology of hyperplane complements and Solomon's descent algebra

J. Matthew Douglass, University of Northern Texas, Denton

February 22, 2011

Math 220

2-3pm

Abstract

Suppose W is a finite Coxeter group. In this talk I'll explain a conjectural relation between (1) the representation of W on the cohomology of the complement of the arrangement of W and (2) the regular representation of W via the descent algebra of W. It is expected that both the group algebra of W and the cohomology of the complement can be decomposed into a sum of induced one-dimensional representations of element centralizers, one for each conjugacy class of elements of W. The conjecture is known to be true for symmetric groups, dihedral groups, and is being checked for all low rank Coxeter groups using GAP and CHEVIE. This is joint work with Gerhard Riehrle and Goetz Pfeiffer.