10 problems

Speculation on the shifted representation. For every $z\in P$, there is an isomorphism of $\mathcal{H}_I$-modules

Let $\mathbf{G}$ be a reductive group defined and split over a $p$-adic field $F$ with residue field $\mathbb{F}_q$. Let $O_F$ be the ring of integers of $F$, set…

Special-orbit conjecture. The representation $\Gamma_{A,1}$ is a model for the universal principal series $\textup{ind}_B^G\chi_{\textup{univ}}^{-1}$ satisfying the diagram relatin…

Gelfand–Graev interpolating-family conjecture. There exists such a family for which

Let $d$ be a positive integer, let ${\mathbf G}$ be a connected reductive group with Frobenius endomorphism $F$, and let ${\mathcal H}^{\mathbf G}_{(d)}$ and…

Let ${\mathbf G}$ be a connected reductive group with Frobenius endomorphism $F$, let ${\mathbf L}$ be an $F$-stable Levi subgroup of a parabolic subgroup, and let…

Let ${\mathbf G}$ be a connected reductive group with Frobenius endomorphism $F$, let ${\mathbf L}$ be an $F$-stable Levi subgroup of a parabolic subgroup ${\mathbf P}$, and let…

Unrestricted Gelfand–Graev restriction conjecture. The same equality should hold without any restriction on $p$, $q$, $F$, or the centre of ${\mathbf L}$. The source states that th…

Let ${\mathbf G}$ be a connected reductive group with Frobenius endomorphism $F$, let ${\mathbf L}$ be an $F$-stable Levi subgroup of a parabolic subgroup ${\mathbf P}$ of…

Let ${\mathbf G}$ be a connected reductive group with Frobenius endomorphism $F$, let $d$ be a positive integer, and let $(K,{\mathcal O},k)$ be a sufficiently large $\ell$-modular…