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Deformations of permutation representations of Coxeter groups

Rains, Eric M. and Vazirani, Monica J. (2013) Deformations of permutation representations of Coxeter groups. Journal of Algebraic Combinatorics, 37 (3). pp. 455-502. ISSN 0925-9899. doi:10.1007/s10801-012-0371-3. https://resolver.caltech.edu/CaltechAUTHORS:20130426-134058196

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Abstract

The permutation representation afforded by a Coxeter group W acting on the cosets of a standard parabolic subgroup inherits many nice properties from W such as a shellable Bruhat order and a flat deformation over ℤ[q] to a representation of the corresponding Hecke algebra. In this paper we define a larger class of “quasiparabolic” subgroups (more generally, quasiparabolic W-sets), and show that they also inherit these properties. Our motivating example is the action of the symmetric group on fixed-point-free involutions by conjugation.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1007/s10801-012-0371-3DOIArticle
http://link.springer.com/article/10.1007/s10801-012-0371-3PublisherArticle
http://rdcu.be/wcbdPublisherFree ReadCube access
https://arxiv.org/abs/1008.1037arXivDiscussion Paper
Additional Information:© 2012 Springer Science+Business Media, LLC. Received: 26 January 2011. Accepted: 6 April 2012. Published online: 28 April 2012. First author partially supported by NSF grant DMS-0833464. Second author partially supported by NSA grant H982300910076, and by Caltech and DMS-0833464 during her visits.
Funders:
Funding AgencyGrant Number
NSFDMS-0833464
National Security AgencyH982300910076
CaltechUNSPECIFIED
Subject Keywords: Coxeter group; Permutation representation; Hecke algebra; Bruhat order
Issue or Number:3
DOI:10.1007/s10801-012-0371-3
Record Number:CaltechAUTHORS:20130426-134058196
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20130426-134058196
Official Citation:Deformations of permutation representations of Coxeter groups Eric M. Rains, Monica J. Vazirani pp.455-502
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:38136
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:26 Apr 2013 21:08
Last Modified:09 Nov 2021 23:33

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