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arXiv · 1008.1037

Deformations of permutation representations of Coxeter groups

Eric M. Rains·Monica J. Vazirani
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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.

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Eric M. Rains, Monica J. Vazirani. 2010-08-05. Deformations of permutation representations of Coxeter groups. https://arxiv.org/abs/1008.1037

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