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The module of affine descents

Abstract : The goal of this paper is to introduce an algebraic structure on the space spanned by affine descent classes of a Weyl group, by analogy and in relation to the structure carried by ordinary descent classes. The latter classes span a subalgebra of the group algebra, Solomon's descent algebra. We show that the former span a left module over this algebra. The structure is obtained from geometric considerations involving hyperplane arrangements. We provide a combinatorial model for the case of the symmetric group.
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https://hal.inria.fr/hal-01229711
Contributor : Alain Monteil <>
Submitted on : Tuesday, November 17, 2015 - 10:20:24 AM
Last modification on : Thursday, July 4, 2019 - 2:10:03 PM
Long-term archiving on: : Thursday, February 18, 2016 - 11:42:44 AM

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Marcelo Aguiar, Kile T. Petersen. The module of affine descents. 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013), 2013, Paris, France. pp.277-288. ⟨hal-01229711⟩

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