Cohomology of Coxeter arrangements and Solomon’s descent algebra
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- by J. Matthew Douglass, Götz Pfeiffer and Gerhard Röhrle PDF
- Trans. Amer. Math. Soc. 366 (2014), 5379-5407 Request permission
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 $A$.References
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Additional Information
- J. Matthew Douglass
- Affiliation: Department of Mathematics, University of North Texas, Denton, Texas 76203
- Email: douglass@unt.edu
- Götz Pfeiffer
- Affiliation: School of Mathematics, Statistics and Applied Mathematics, National University of Ireland Galway, Galway, Ireland
- Email: goetz.pfeiffer@nuigalway.ie
- Gerhard Röhrle
- Affiliation: Fakultät für Mathematik, Ruhr-Universität Bochum, D-44780 Bochum, Germany
- MR Author ID: 329365
- Email: gerhard.roehrle@rub.de
- Received by editor(s): July 16, 2012
- Received by editor(s) in revised form: December 4, 2012
- Published electronically: June 19, 2014
- Additional Notes: The authors would like to thank their charming wives for their unwavering support during the preparation of this paper.
- © Copyright 2014
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 366 (2014), 5379-5407
- MSC (2010): Primary 20F55; Secondary 05E10, 52C35
- DOI: https://doi.org/10.1090/S0002-9947-2014-06060-1
- MathSciNet review: 3240927