6 problems

Let $G'$ and $G$ be the members of a reductive dual pair, and let $obreakomega^infty$ denote the smooth oscillator representation. For smooth irreducible representations ${pi}'$ a…

Let $\pi$ be a representation in $\mathrm{Rep}^{\infty,F}(M_{n+1})$, and suppose that $\pi$ is nuclear. Let $\pi_k$ denote the terms of the filtration from Theorem 1, whose constru…

Let $\mathbb{H}$ be the Drinfeld upper-half space, let $H^{i}_{\operatorname{HK}}(\mathbb{H})$ denote its Hyodo–Kato cohomology, and let $V_{[1,n-1-i]}^{\infty}$ and…

Let $F$ be a non-archimedean local field, let $G$ be the $F$-points of a connected reductive split algebraic group over $F$, and let $\mathfrak{s}$ be a Bernstein component. Let…

Geometric structure conjecture. After a simple algebraic deformation, the space ${\mathfrak A}(G)$ is a model of the smooth dual ${\rm Irr}(G)$.

Ext comparison conjecture.