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I'm trying to better understand the continuous spectrum of $G = \operatorname{GL}_2(\mathbb A_{\mathbb Q})$, which is the direct integral of induced representations $\mathbf H(s) = \operatorname{Ind}_{...

Let $G$ be the $\mathbf{Q}_p$-points in a $p$-adic reductive group, and let $R(G)$ be the Grothendieck group of the category $\mathrm{Rep}(G)$ of finite-length admissible smooth complex ...

A common way of doing harmonic analysis on (the $\mathbb{R}$-points of) reductive groups over $\mathbb{R}$ seems to be to use results from semisimple groups and "see what happens on the center&...

Let $G$ be a connected, reductive group over a $p$-adic field $k$, $A_0$ a maximal split torus of $G$, and $P = MU$ a parabolic subgroup with $M$ containing $A_0$. Let $\overline{P} = M \overline{U}$ ...