Flip actions and Gelfand pairs for affine Weyl groups

Abstract

Several combinatorial actions of the affine Weyl group of type ${\tilde{C}}_n$ 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 ${\tilde{C}}_n$ and ${\tilde{B}}_n$.

26 pages, various changes and improvements

References in corpus (3)

• On the center of the Hurwitz graph
• Flip Graphs, Yoke Graphs and Diameter
• Convex caterpillars are Schur-Positive

Cited by in corpus (1)

• Gelfand pairs for affine Weyl groups