4 problems

Let $G_{q\widetilde{q}}^+(\mathbb{R})$ be the positive quantum group associated with $\mathfrak{g}_\mathbb{R}$, and let $L^2(G_{q\widetilde{q}}^+(\mathbb{R}))$ carry the left and r…

Let $Y=H\backslash G$ be a strongly tempered spherical variety over a local field $F$. Let $G_Y^\vee$ be the dual group of $Y$, let…

Let $\Pi$ be a class of representations appearing in the Plancherel theorem, and let $\Omega$ be the map from such classes to two-sided cells; write $\Gamma=\Omega(\Pi)$. Let…

Let $\Pi$ range over the classes of representations appearing in the Plancherel formula, and let the two-sided cells be the cells of the affine Hecke algebra. A Plancherel-to-cell…