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Flip actions and Gelfand pairs for affine Weyl groups (2009.13880v2)
Published 29 Sep 2020 in math.CO
Abstract: Several combinatorial actions of the affine Weyl group of type $\widetilde{C}{n}$ 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 $\widetilde{C}{n}$ and $\widetilde{B}_n$.
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