3 problems

Let $G$ be a reductive group, let $X$ be a curve over a local field $F$, and let $\lambda\ne0$. Write $V_G(\lambda)$ for the dense domain on which the Hecke operators are initially…

Basic spectral decomposition conjecture. The Hilbert space has an orthogonal decomposition

Second analytic Langlands conjecture. The spectrum $\operatorname{Spec}_{\mathcal A}(\mathcal H)$ is discrete; equivalently, $\mathcal H$ is the completed direct sum of finite-dime…