An Inductive Approach to Coxeter Arrangements and Solomon's Descent Algebra
Representation Theory
2011-06-14 v2 Combinatorics
Group Theory
Abstract
In a recent paper we claimed that both the group algebra of a finite Coxeter group as well as the Orlik-Solomon algebra of can be decomposed into a sum of induced one-dimensional representations of centralizers, one for each conjugacy class of elements of , and gave a uniform proof of this claim for symmetric groups. In this note we outline an inductive approach to our conjecture. As an application of this method, we prove the inductive version of the conjecture for finite Coxeter groups of rank up to 2.
Keywords
Cite
@article{arxiv.1104.0551,
title = {An Inductive Approach to Coxeter Arrangements and Solomon's Descent Algebra},
author = {J. Matthew Douglass and Goetz Pfeiffer and Gerhard Roehrle},
journal= {arXiv preprint arXiv:1104.0551},
year = {2011}
}
Comments
21 pages; to appear in J. Algebraic Combin