Cohomology of Coxeter arrangements and Solomon's descent algebra

@article{Douglass2011CohomologyOC,
  title={Cohomology of Coxeter arrangements and Solomon's descent algebra},
  author={J. Matthew Douglass and Goetz Pfeiffer and Gerhard R{\"o}hrle},
  journal={arXiv: Representation Theory},
  year={2011}
}
We refine a conjecture by Lehrer and Solomon on the structure of the Orlik-Solomon algebra of a finite Coxeter group $W$ and relate it to the descent algebra of $W$. As a result, we claim that both the group algebra of $W$, as well as the Orlik-Solomon algebra of $W$ can be decomposed into a sum of induced one-dimensional representations of element centralizers, one for each conjugacy class of elements of $W$. We give a uniform proof of the claim for symmetric groups. In addition, we prove that… 
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