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On Twisted Gelfand Pairs Through Commutativity of a Hecke Algebra

On Twisted Gelfand Pairs Through Commutativity of a Hecke Algebra

For a locally compact, totally disconnected group $G$, a subgroup $H$ and a character $\chi:H \to \mathbb{C}^{\times}$ we define a Hecke algebra $\mathcal{H}_\chi$ and explore the connection between commutativity of $\mathcal{H}_\chi$ and the $\chi$-Gelfand property of $(G,H)$, i.e. the property $\mathrm{dim}_\mathbb{C}(\rho^*)^{(H,\chi^{-1})} \leq 1$ for every $\rho \in \mathrm{Irr}(G)$, the irreducible …