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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… Click to show full 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 $\widetilde{B}_n$.
Keywords:
actions gelfand;
affine weyl;
combinatorial flip;
gelfand pairs;
weyl groups;
flip actions
Journal Title: Journal of Algebra
Year Published: 2021
Link to full text (if available)
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Journal Title: Journal of Algebra
Year Published: 2021
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!