12 problems

Let $\mathbb{Z}[i]$ be the Gaussian integers, let $\widetilde{g}_4(\pi)$ denote the quartic Gauss sum attached to a prime $\pi$, let $N(\pi)$ be its norm, and let $\tau_4(\pi)$ be…

Let $n$ be a positive integer. Consider the $n$-cover of $GL(n,\mathbb C)$ and the Eisenstein series obtained by inducing the theta function on the $n$-cover of $GL(n-1,\mathbb C)$…

Eisenstein conjecture. The Whittaker coefficients of a metaplectic Eisenstein series are Weyl group multiple Dirichlet series; in the setting above, the first Whittaker coefficient…

There is a metaplectic spherical Whittaker function, denoted $\widetilde{\mathcal{W}}^{m} = \widetilde{\mathcal{W}}^{m}(\mathbf{y}; g;v)$, and components…

Let $F$ be a non-archimedean local field, and consider the solvable lattice model constructed by Brubaker et al. for the double cover of $\mathrm{Sp}(2n,F)$. Its partition function…

Consider the lattice models and Whittaker functions with colors and supercolors, together with the Iwahori-metaplectic duality discussed in the paper. Parahoric-metaplectic duality…

Let $F$ be the number field in the setting, let $\widetilde{\pi}$ be an irreducible cuspidal automorphic representation of the metaplectic double cover…

Let $n$ be odd, let $r$ be a positive integer, and let $Z_{\lambda}(\mathbf{z};\mathbf{c})$ be the partition function of the symplectic-ice model with partition boundary data deter…

Let $G^\vee$ be the dual group, let $P$ be a parabolic subgroup, and let $\boldsymbol{i}^P$ be the reduced word associated with $P$. Let $\boldsymbol{m}$ be the highest weight of a…

Odd-degree conjecture. The integer $n$ should be odd.

Type C multiple-Dirichlet-series conjecture. The series $Z_\Psi(\mathbf{s};\mathbf{m})$ should have meromorphic continuation to $\mathbb{C}^r$ and satisfy a group of functional equ…

Metaplectic Eisenstein-series conjecture. The families of multiple Dirichlet series associated to $\Phi$ should be precisely the Fourier–Whittaker coefficients of minimal parabolic…