9 problems

Let $F$ be a local field of characteristic zero, let $E/F$ be a quadratic étale algebra, and let $\psi$ be a non-trivial character of $F$. Let $\eta_{E/F}$ be the quadratic charact…

Let $K/k$ be a quadratic extension of number fields, let $\mathbb{H}^\circ$ be a $k$-quasisplit classical group, and let $T$ be the functorial lift to…

Epsilon dichotomy conjecture.

Let $E/{\mathcal F}$ be the quadratic extension implicit in the distinction notation, with $n\ge3$. Let $\pi$ be a supercuspidal representation of $\operatorname{GL}_n(E)$, and for…

Let $F$ be a nonarchimedean local field, let $E/F$ be a quadratic extension, and let $\tau$ be a square-integrable representation of $\mathrm{PGSp}_4(E)$. A representation is…

Unitary-symplectic distinction conjecture. Some member of $\{\pi\}$ is distinguished by $\operatorname{Sp}_{2n}(F)$ if and only if $BC(\pi)$ is distinguished by…

Tempered distinction conjecture. There are tempered representations of $\operatorname{SO}(V)$ distinguished by $\operatorname{SO}(W)$ if and only if

Let $F$ be a nonarchimedean local field with finite residual field, let $E/F$ be a Galois quadratic extension, and let $G$ be a connected reductive group defined over $F$. Write…

Let $F_v$ be a local field, let $D_v$ be a quaternion division algebra over $F_v$, and let $H_v$ and $H'_v$ be the relevant subgroups of $\operatorname{GL}_n(D_v)$ and…