An inductive approach to coxeter arrangements and solomon's descent algebra

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Date
2011-05-17MFO Scientific Program
Research in Pairs 2010Series
Oberwolfach Preprints;2011,16Author
Douglass, J. Matthew
Pfeiffer, Götz
Röhrle, Gerhard
Metadata
Show full item recordOWP-2011-16
Abstract
In our recent paper [3], 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 nite Coxeter groups of rank up to 2.