Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Cohomology of Coxeter arrangements and Solomon's descent algebra

Authors: J. Matthew Douglass, Götz Pfeiffer and Gerhard Röhrle
Journal: Trans. Amer. Math. Soc. 366 (2014), 5379-5407
MSC (2010): Primary 20F55; Secondary 05E10, 52C35
Published electronically: June 19, 2014
MathSciNet review: 3240927
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 20F55, 05E10, 52C35

Retrieve articles in all journals with MSC (2010): 20F55, 05E10, 52C35

Additional Information

J. Matthew Douglass
Affiliation: Department of Mathematics, University of North Texas, Denton, Texas 76203

Götz Pfeiffer
Affiliation: School of Mathematics, Statistics and Applied Mathematics, National University of Ireland Galway, Galway, Ireland

Gerhard Röhrle
Affiliation: Fakultät für Mathematik, Ruhr-Universität Bochum, D-44780 Bochum, Germany

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.
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society