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Let $G$ be a compact topological group. By the Peter-Weyl theorem, the complex Hilbert space $L^2(G)$ is the Hilbert space direct sum of the spaces of matrix coefficients of all the irreducible ...

Let $F$ be a non-Archimedean local field (characteristic 0) and $G=GL(2,F)$. Let $\tilde{G}$ be "the" metaplectic double cover of $G$ (defined using an explicit cocycle as in Gelbart's book (Weil's ...

Let $E$ and $F$ be finite extensions of $\mathbb{Q}_p$. Let $\phi:\mathrm{Gal}(\overline{E}/E)\to GL_n(F)$ be an absolutely irreducible continuous representation. Assume that the restriction of $\phi$ ...