Comparison conjecture for quantum and elliptic cuspidal modules

Let $G$ be a connected reductive group, let $E$ be an elliptic curve, and let $\operatorname{Bun}_G^{ss,0}(E)$ denote the moduli stack of semistable degree-zero $G$-bundles on $E$. Consider simple cuspidal ${\mathcal D}_\mathtt{q}(G)$-modules and simple cuspidal generically twisted $\mathcal D$-modules on $\operatorname{Bun}_G^{ss,0}(E)$. Quantum–elliptic cuspidal comparison conjecture. There is a natural bijection between these two sets of simple cuspidal modules. The conjecture compares the cuspidal data governing the quantum and elliptic generalized Springer decompositions, although the categorical structures of the individual blocks differ.