35 problems

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…

Fix a distinguished character $\overline{\chi}^0$. Let $\mathcal{A}_\epsilon(\overline{\operatorname{Sp}}_{2r}(\mathbb A))$ denote the relevant discrete-spectrum representation spa…

Let $\widetilde{G}$ be the metaplectic cover and $(\widetilde{J},\widetilde{\lambda})$ the type constructed in the paper. Let $\widetilde{M}$ be the associated Levi subgroup,…

Let $M$ be a Levi subgroup of a reductive group over a non-archimedean locally compact field. A cuspidal representation of $M$ is an irreducible smooth representation whose relevan…

Gray's U-turn lattice models associate a partition function to metaplectic covers of the symplectic group. Gray's conjecture. The partition function is the spherical Whittaker func…

Let $r$ be odd, and let $\rho$ be the representation of $Sp_{2n+r-2k+1}^{(2r)}({\mathbb A})$ generated by the descent functions defined by the integral construction in the paper. D…

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…

Orbit Conjecture. The set ${\mathcal O}(\Theta_{2l}^{(r)})$ is the singleton $\{{\mathcal O}_c(\Theta_{2l}^{(r)})\}$. The vanishing assertion is known, while the required nonvanish…

Let $\mathcal{K}$ be the set of relevant subgroups, let $H_\varphi$ be the image defined in the preceding diagrams, and let \phi_\overline{\overline{\overline{\overline{\chi}}}}…

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…

Let $\overline{M}_{\mathbf r}$ be the covering Levi subgroup with dual inclusion…

Let $\pi^{(n)}$ and $\tau^{(n)}$ be irreducible cuspidal representations of $GL_r^{(n)}({\bf A})$, let $L^S(\pi^{(n)}\times\tau^{(n)},s)$ be the partial tensor product $L$-function…

Let ${\bf A}$ be the ring of adeles, let $\tau$ be an irreducible cuspidal representation of $GL_m({\bf A})$, and let $GL_{nm}^{(n)}({\bf A})$ denote the $n$-fold metaplectic cover…

Non-genericity classification conjecture. Ignoring the special cases mentioned in the paper, $\pi$ is not generic if and only if it is a subrepresentation of

Let $\rho$ denote the action referred to in the source, let $\funct{Wh}$ be the space of Whittaker functionals, and let $\funct{Wh}_{\widetilde{K}}$ be its subspace associated with…

Let $\mathop{\pi}$, $\mathop{\tau}$, and $\mathop{\sigma}\in \operatorname{Wd}_{\psi}(\tau)$ be as in the setup of the local triple product period. Assume that the local nonvanishi…

The local intertwining relation conjecture. Given $\phi_M$ and $u$ as above, one expects

The refined character formula conjecture. One expects

The local Langlands correspondence conjecture. There should be a local Langlands correspondence

Let $F$ be a totally real number field, let $n$ be odd, and let $\pi\simeq\otimes'_v\pi_v$ be an irreducible cuspidal automorphic representation of $\mathrm{PGL}_2(\mathbb A)$ such…

Fundamental lemma. It is conjectured that there is a matching relation between a Hecke function on $S(F)$ and a Hecke function on $\widetilde{\mathrm{GL}}_r(F)$.

Let $G$ be the reductive group with coweight lattice $\Lambda$, let $\Lambda^{\sharp,+}$ be the dominant metaplectic coweights, and let $\gamma\in\Lambda^{\sharp,+}$ and…

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 $A_{p,q}(k)$ denote a middle-dimensional cohomologically induced representation associated with a Levi subgroup $\widetilde{U}(p,q)$ of $Mp_{2n}(\mathbb R)$ or with a Levi subg…