7 problems

Let $G$ be the $p$-adic group under consideration and let $R$ be a field of characteristic different from $p$. A cuspidal irreducible $R$-representation of $G$ is an irreducible re…

Let $F$ be a nonarchimedean local field, let $\boldsymbol{\mathrm{G}}$ be a connected reductive group defined over $F$, and let $G=\boldsymbol{\mathrm{G}}(F)$ with center $Z$. Let…

Let $M$ be a Levi subgroup of a reductive group over a non-archimedean locally compact field. A cuspidal representation of $M$ is an irreducible smooth representation whose relevan…

Compact-modulo-center induction conjecture. Every supercuspidal representation of a $p$-adic group is isomorphic to the compact induction of some finite-dimensional irreducible rep…

Let $F$ be a non-archimedean local field with finite residue field of characteristic $p$, let $\underline G$ be a connected reductive linear group over $F$, let $G=\underline G(F)$…

A supercuspidal representation of a reductive group $\mathcal{G}$ is an irreducible smooth representation that is not a subquotient of any proper parabolically induced representati…

Let $G$ be a connected reductive $p$-adic group. Let $J$ be an open subgroup of $G$ containing the center $Z$ such that $J/Z$ is compact, let $\kappa$ be an irreducible smooth repr…