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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.

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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.

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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.
Funding AgencyGrant Number
National Security AgencyH982300910076
Subject Keywords: Coxeter group; Permutation representation; Hecke algebra; Bruhat order
Issue or Number:3
Record Number:CaltechAUTHORS:20130426-134058196
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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
Deposited By: Ruth Sustaita
Deposited On:26 Apr 2013 21:08
Last Modified:09 Nov 2021 23:33

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