10 problems

Let $F$ be a non-Archimedean local field of characteristic zero, let $l$ be a positive integer, and let $\mathrm{GL}_l(F)$. Let $\pi,\pi'$ be irreducible generic representations of…

Let $\operatorname{E}/\operatorname{F}$ be the setting of distinguished representations, and let $\pi$ be a supercuspidal representation of $\operatorname{GL}(n,\operatorname{E})$…

Let $F$ be the underlying non-Archimedean local field, let $n$ be a positive integer, and let $\pi_{1}$ and $\pi_{2}$ be irreducible supercuspidal representations of…

Local converse conjecture. If

Let $F$ be a local non-Archimedean field, let $n$ be a positive integer, and let $\pi_1$ and $\pi_2$ be irreducible unitarizable supercuspidal representations of…

Let $\ell$ be a prime and let $n$ denote the rank in the mod-$\ell$ representation-theoretic setting. A converse theorem is a result asserting that a representation is determined b…

Let $pi_f$ and $pi_g$ be the representations of $\operatorname{GL}_n$ and $\operatorname{GL}_m$ over the finite field in the source, with corresponding characters $alpha$ and…

Jacquet's conjecture. If $\pi_1$ and $\pi_2$ satisfy $\mathcal H_{\leq r}$, then $\pi_1\simeq\pi_2$.

Local converse conjecture. If $\pi_1$ and $\pi_2$ have the same central character and

Let $F$ be a locally compact non-archimedean local field, let ${\mathrm{G}}_n={\mathrm{GL}}_n(F)$, and let $\psi$ be a nontrivial additive character of $F$. Assume that $\pi_1$ and…