Peer-Reviewed Journal Details
Mandatory Fields
Douglass, JM,Pfeiffer, G,Rohrle, G
2012
March
Journal Of Algebraic Combinatorics
An inductive approach to Coxeter arrangements and Solomon's descent algebra
Published
()
Optional Fields
Coxeter groups Reflection arrangements Descent algebra Dihedral groups PARABOLIC SUBGROUPS
35
215
235
In our recent paper (Douglass et al. arXiv: 1101.2075 (2011)), 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.
DOI 10.1007/s10801-011-0301-9
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