Journal of Algebraic Combinatorics

, Volume 35, Issue 2, pp 215–235 | Cite as

An inductive approach to Coxeter arrangements and Solomon’s descent algebra

  • J. Matthew Douglass
  • Götz Pfeiffer
  • Gerhard Röhrle


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.


Coxeter groups Reflection arrangements Descent algebra Dihedral groups 


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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • J. Matthew Douglass
    • 1
  • Götz Pfeiffer
    • 2
  • Gerhard Röhrle
    • 3
  1. 1.Department of MathematicsUniversity of North TexasDentonUSA
  2. 2.School of Mathematics, Statistics and Applied MathematicsNational University of IrelandGalwayIreland
  3. 3.Fakultät für MathematikRuhr-Universität BochumBochumGermany

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