J. Matthew Douglass, Götz Pfeiffer, and Gerhard Röhrle,
In a recent paper we claimed that both the group algebra of a finite Coxeter groupW as well as the Orlik-Solomon algebra ofW can be decomposed into a sum of induced one-dimensional representations of centralizers, one for each conjugacy class of elements ofW , 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 to2 .
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