Logarithmic Kazhdan–Lusztig conjecture for kernels of screening operators

Let $\mathcal{V}$ be a vertex algebra, let $\mathfrak{Z}_{\mathcal{M}_1},\ldots,\mathfrak{Z}_{\mathcal{M}_n}$ be screening operators, and let $\mathcal{W}\subset\mathcal{V}$ be their common kernel. Write $\operatorname{Rep}(\mathcal{V})$ for the representation category of $\mathcal{V}$, and let $\mathcal{YD}^{\mathfrak{B}}_{\mathfrak{B}}(\operatorname{Rep}(\mathcal{V}))$ denote the generalized quantum group associated with the relevant Nichols algebra. Logarithmic Kazhdan–Lusztig conjecture. Under suitable assumptions, the category of representations of $\mathcal{W}$ is given by the generalized quantum group $\mathcal{YD}^{\mathfrak{B}}_{\mathfrak{B}}(\operatorname{Rep}(\mathcal{V}))$. This is presented as the author's version of the logarithmic Kazhdan–Lusztig conjecture; the notes do not specify the assumptions or provide evidence of resolution.