3 problems

Let $\widetilde K$ be the spin cover of a maximal compact subgroup $K$, and let $\mathsf{I}_{\mathrm{Dir}}(X)$ denote the Dirac index of a finite-length Harish-Chandra module $X$.…

Let $G$ be a real reductive group with the notation above, let $G_{\mathrm{ell}}$ be the regular semisimple elliptic elements, let $C^{\mathrm{ell}}$ be the set of regular semisimp…

Let $\mathbf{L}$ be a connected reductive group over a non-archimedean local field $\mathbb F$, let $L=\mathbf{L}(\mathbb F)$, and assume that $\mathbb F$ has characteristic $0$. L…