28 problems

Let $E/F$ be a quadratic extension, let $G$ be a reductive group over $F$, and let $N_0$ be the unipotent subgroup associated with a fixed Whittaker datum. Let $\pi$ be an irreduci…

Let $\tilde{\varphi}_0:X_{Q,n}/X_{Q,n}^{sc}\to X/X_G^{sc}$ be well-defined, let $\mathfrak{w}=(B,U,\psi)$ be Whittaker data, and let…

Let $F$ be either ${\mathbb R}$ or a finite extension of ${\mathbb Q}_p$, let $G$ be a finite central extension of the group of $F$-points of a connected reductive algebraic group…

Let $F$ be a non-Archimedean local field, let $G=\operatorname{GL}_{2n}(F)$, and let $P_{n,n}=MN$ be the standard parabolic subgroup with Levi factor…

Let $G$ be a non-commutative group. Recall that $\Whit(G):=\Whit(\Dmod(\operatorname{Gr}_G))$ is the factorization category obtained from the Whittaker model of the category of $D$…

Let $G$ be a quasi-split connected reductive group over $\mathbb Q$, let $N$ be the unipotent radical of a Borel subgroup, and fix a non-degenerate character $\psi_N$ of…

Let $G_n=\mathrm{GL}_n(F)$, let $\lambda$ be the relevant orbit parameter, and let $W_{\lambda}$ be the associated space of degenerate Whittaker functions. Gomez–Gourevitch–Sahi co…

p-adic analogue conjecture. These properties should hold in the $p$-adic case as well.

Let $F$ be a nonarchimedean local field with ring of integers $\mathfrak{o}$, and let $\mathfrak{o}_l=\mathfrak{o}/(varpi^l)$. Let $L$ and $E$ be unramified extensions of $F$ of de…

Whittaker-space isomorphism conjecture. For every $W$-orbit $\mathcal{O}\subset\mathscr{X}_{Q,n}$, the embedding is an isomorphism

Let $r>1$ be odd, let $F$ be a global field, and let $\Theta_{r-1}^{(r)}$ be the theta representation of the $r$-fold metaplectic cover of $Sp_{r-1}({\mathbb A})$. Put…

Let $\overline{G}_0$ be a saturated cover, let $\mathscr{X}_{Q,n}$ be the relevant lattice, and let $\mathscr{X}_{0,Q,n}$ be the Weyl-stable sublattice. Let $W$ act by the usual We…

A representation in the space of automorphic forms is said to have Gelfand–Kirillov dimension $d$ if all the orbits in its Whittaker support have dimension $2d$. Gelfand–Kirillov d…

Let $\overline{G}$ be an $n$-fold persistent covering group. Let $\Theta(\overline{G},\chi)=\pi_{\Gamma^-}$ be the theta representation associated to an unramified character $\chi$…

In the situation of Theorem, let $F_G(K_{E,\chi, \mathbb H})$ be the complex on $\operatorname{Bun}_{\mathbb G}$ constructed there, and let $\Whit$ denote the first Whittaker coeff…

Let $F$ be Archimedean, let $G$ be a finite central extension of the group of $F$-points of a connected reductive algebraic group defined over $F$, and let…

Archimedean wave-front/Whittaker-support conjecture. The same two assertions should hold for Archimedean $F$. This would extend the established non-Archimedean comparison between w…

Let $\pi$ be a generic cuspidal representation of $\overline{\operatorname{Sp}}_{2r}$, and let $n(\pi)$ denote the invariant introduced in the discussion of Whittaker coefficients.…

Whittaker vanishing conjecture. If $J$ satisfies this dimension equation, then $J$ is zero for every choice of data.

Let $x$ be a point of the curve, let $\Whit_x^\kappa$ be the metaplectic Whittaker category at $x$, and let $\mathcal F_{x,\mu}$ denote the Whittaker object indexed by a dominant c…

Let $\rho$ be the quadratic form on the coweight lattice associated with the metaplectic data. For $\bar c$ the residue-field point and $\bar\theta$ the image of $\theta$ in the ad…

Let $G$ be a reductive group, let $\mathcal{O}$ be a nilpotent orbit, and let $\mathcal{W}_{\mathcal{O}}$ denote the generalized Whittaker functor assigning to a representation…

Classical-group descent conjecture. If $\pi$ is an irreducible constituent of $\sigma^{\psi_N}(\{\pi_1,\dots,\pi_k\})$, then

Let $G$ be a connected reductive group, let $\operatorname{Bun}_G$ be its moduli stack of bundles, and let $\operatorname{Whit}^{\operatorname{ext}}(G,G)$ be the extended Whittaker…

Whittaker and theta-lifting conjecture. (i) $\mathcal K_E$ is a perverse sheaf, each of whose $\mathbb Z/2\mathbb Z$-parity pieces is irreducible, and