Marcelo Aguiar ; Kile T. Petersen - The module of affine descents

dmtcs:12811 - Discrete Mathematics & Theoretical Computer Science, January 1, 2013, DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013) - https://doi.org/10.46298/dmtcs.12811
The module of affine descentsArticle

Authors: Marcelo Aguiar 1; Kile T. Petersen 2

  • 1 Department of Mathematics [Austin]
  • 2 Department of Mathematical Sciences [Chicago]

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.


Volume: DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013)
Section: Proceedings
Published on: January 1, 2013
Imported on: November 21, 2016
Keywords: Weyl group,Coxeter complex,hyperplane arrangement,Tits product,Solomon's descent algebra,Steinberg torus,[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]

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