Flip actions and Gelfand pairs for affine Weyl groups

2020/09/29 by Ron M. Adin, Adin, Ron M., Pál Hegedüs +3
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2009.13880

openalex publication_date 2020/09/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Several combinatorial actions of the affine Weyl group of type \widetildeC_n on triangulations, trees, words and permutations are compared. Addressing a question of David Vogan, we show that, modulo a natural involution, these permutation representations are multiplicity-free. The proof uses a general construction of Gelfand subgroups in the affine Weyl groups of types \widetildeC_n and \widetildeB_n.

Citations

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