# 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}
}
• Published 11 January 2011
• Mathematics
• arXiv: Representation Theory
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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## References

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• Mathematics
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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
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