论文标题
仿生基团的翻转动作和gelfand对
Flip actions and Gelfand pairs for affine Weyl groups
论文作者
论文摘要
比较了三角形，树，单词和置换的类型$ \ widetilde {c} _ {n} $类型的杂物weyl组的几种组合动作。在解决大卫·沃根（David Vogan）的问题时，我们表明，这些置换表示形式是自然的，这些置换表示不含多重性。证明使用类型$ \ widetilde {c} _ {n} $和$ \ widetilde {b} _n $的类型的offine Weyl组中Gelfand子组的一般结构。
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 $\widetilde{B}_n$.
