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Published May 2013 | Submitted
Journal Article Open

Deformations of permutation representations of Coxeter groups

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.

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.

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August 22, 2023
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