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
DOI:
https://doi.org/10.1090/S0002-9947-2014-06060-1
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 and relate it to the descent algebra of
. As a result, we claim that both the group algebra of
and the Orlik-Solomon algebra of
can be decomposed into a sum of induced one-dimensional representations of element centralizers, one for each conjugacy class of elements of
. 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
, where
is arbitrary and
is a parabolic subgroup of
, all of whose irreducible factors are of type
.
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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
Email:
gerhard.roehrle@rub.de
DOI:
https://doi.org/10.1090/S0002-9947-2014-06060-1
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.