6 problems

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…

Let ${\bf Y}$ be an $F$-quasi-split group, let $E/F$ be the quadratic extension implicit in the notation, and let $\mathbf{BC}_F^E$ denote the base-change map from $L$-parameters o…

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…

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

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…