3 problems

C-group Galois representation conjecture. There exists an admissible representation

Let $X$ be a strongly tempered spherical variety, so that its dual group satisfies $\check{G}_X=\check{G}$. Let $\mathbf{A}=\mathbf{A}_X$, let $\delta$ denote the relevant modular…

Semi-infinite extension conjecture. If $\CF$ is the constant sheaf on $G_{\sO}$, then $f_{i_{!*}\CF}$ corresponds under the Satake isomorphism to…