7 problems

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…

Cauchy Harish-Chandra character correspondence conjecture. Assuming the character conjecture referred to in the source, define

Bernon–Przebinda's conjecture. Up to a constant, … on $\widetilde{{\rm G}'_{1}}$.

Inverse-rank conjecture. Then

Let $G=\mathbf{GL}_{n}$ and $H=\mathbf{GL}_{m}$ with $n\leq m$. Let $K(\mathcal{X})$ and $K(DP_{I_{H}\times I_{G}}(\Pi(F)))$ be the associated bimodules under the extended affine H…

Let $(G,H)$ be a dual split reductive pair over $\mathbf{k}$, let $\mathcal{W}$ be the graded Weil category, and let $(D\mathcal{W})^{I_{G}\times I_{H}}$ denote its…

Let $(G,H)$ be a dual split reductive pair over $\mathbf{k}$, let $\mathcal{W}$ be the Weil category equipped with an action of $(G\times H)(F)$, and let $\mathcal{C}_{G}$ and…