Varagnolo–Vasserot's quotient conjecture for Schur categories

Fix $e,\ell,m>0$ and let $\nu\in\mathbb{N}^{\ell}(m)$. Let $\mathcal{O}^{\nu}(n)$ be the affine category block decomposition introduced in the source, let $\mathbf{S}^{\nu}(n)$ be the thick subcategory of $\mathbf{O}^{\nu}$ consisting of finite-length modules whose constituents are among $\{L_e^{\nu}(\lambda)\mid\lambda\in P(\nu,n)\}$, and let $S_e^{\nu}(\lambda)$ and $L_e^{\nu}(\lambda)$ denote the standard and simple objects defined there. Varagnolo–Vasserot's conjecture. There is a quotient functor

$$\mathcal{O}^{\nu}(n)\to\mathbf{S}^{\nu}(n)$$

taking $S_e^{\nu}(\lambda)$ to $L_e^{\nu}(\lambda)$ if $\lambda\in P(\nu,n)$ and to $0$ otherwise. If $P(\nu,n)=P(n)$, this functor is an equivalence of highest weight categories. The conjecture concerns the relationship between affine category $\mathcal{O}$ and the corresponding Schur category; the source gives no resolution status.