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arXiv · 2009.13880

Flip actions and Gelfand pairs for affine Weyl groups

Ron M. Adin·Pál Hegedüs·Yuval Roichman
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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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Ron M. Adin, Pál Hegedüs, Yuval Roichman. 2021-11-29. Flip actions and Gelfand pairs for affine Weyl groups. https://arxiv.org/abs/2009.13880

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