4 problems

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…

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…