An Inductive Approach to Coxeter Arrangements and Solomon's Descent Algebra

Details An Inductive Approach to Coxeter Arrangements and Solomon's Descent Algebra An Inductive Approach to Coxeter Arrangements and Solomon's Descent Algebra

2011-04-04

arxiv.org/abs/1104.0551v2

Mathematics

Representation Theory

21 pages; to appear in J. Algebraic Combin

Scientific paper

In a recent paper we claimed that both the group algebra of a finite Coxeter group $W$ as well as the Orlik-Solomon algebra of $W$ can be decomposed into a sum of induced one-dimensional representations of centralizers, one for each conjugacy class of elements of $W$, 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.

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