## Cohomology of Coxeter arrangements and Solomon's descent algebra

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2014-06-19##### Author

Douglass, J. Matthew

Pfeiffer, Götz

Röhrle, Gerhard

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##### Recommended Citation

Douglass, JM,Pfeiffer, G,Rohrle, G (2014) 'COHOMOLOGY OF COXETER ARRANGEMENTS AND SOLOMON'S DESCENT ALGEBRA'. Transactions Of The American Mathematical Society, 366 :5379-5407, doi:10.1090/S0002-9947-2014-06060-1

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##### Abstract

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 and 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 a relative version of the conjecture holds for every pair (W, W-L), where W is arbitrary and W-L is a parabolic subgroup of W, all of whose irreducible factors are of type A.