4 problems

Let $G$ be a reductive group with Langlands dual group $G^\vee$, and let $W$ be the Weyl group. Let $X$ be a smooth spherical $G$-variety such that $T^*X$ is hyperspherical and has…

Let $G$ be a complex reductive group, let $X$ be a smooth affine spherical $G$-variety with connected stabilizers in the open Borel orbit, and set $M=T^*(2)(X)$. Let…

Assume that $\check{M}=T^*\check{X}$, where $\check{X}$ is a $\check{G}$-spherical variety. Let $\pi$ be a tempered, everywhere unramified automorphic representation of…

Dolbeault S-duality matching conjecture. Over the $\diamondsuit$-locus, the following matching data hold under $\mathbf{S}_{\mathrm{Dol}}$: the dual of $A_{\mathrm{Dol}}(M_\rho')$…