The extended Whittaker coefficient conjecture

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 category. Let

$$\operatorname{coeff}^{\operatorname{ext}}_{G,G}:\operatorname{Dmod}(\operatorname{Bun}_G)\to \operatorname{Whit}^{\operatorname{ext}}(G,G)$$

be the extended Whittaker coefficient functor. Extended Whittaker coefficient conjecture. The functor $\operatorname{coeff}^{\operatorname{ext}}_{G,G}$ is fully faithful. This conjecture is one of the principal supporting assertions for geometric Langlands; the source notes that it is a quasi-theorem for $GL_n$, and a theorem for $n=2$.