The l-adic Whittaker-sheaf equivalence conjecture

Let $G$ be a reductive group, let $U$ be the unipotent radical of a Borel subgroup, and let $T$ be the corresponding maximal torus. Fix a non-degenerate homomorphism $\chi:U\to\mathbb G_a$, and let an $\ell$-adic Whittaker sheaf on $G$ be a perverse sheaf with the stated $(U\times U,\chi)$-equivariance structure. The $\ell$-adic Whittaker-sheaf equivalence conjecture. There is an equivalence

$$\text{the category of $\ell$-adic Whittaker sheaves on $G$}\simeq\text{the category of central perverse sheaves on $T$}.$$

This is proposed as the $\ell$-adic counterpart of the preceding de Rham equivalence for Whittaker $D$-modules. The source gives no resolution status.