3 problems

Let $G$) and $G^{\prime}$ be mutual centralizers forming a reductive dual pair inside a symplectic group over a local field $F$. Let $\omega$ be an oscillator representation of the…

Stable-range theta lift low-rank conjecture. The theta lift $\theta(\tau)$ is a low rank representation of $G$, meaning that its $U$-support contains no open $L$-orbit.

Let $(\mathrm{G},\mathrm{G}')$ be a reductive dual pair over a non-Archimedean local field, let $\Pi'$ be an irreducible admissible representation of $\widetilde{\mathrm{G}'}$ occu…