6 problems

Let $ell$ be an admissible level for the simple Lie algebra $\bf g$. Vertex tensor and ribbon category conjecture. 1. $L_{ell}(\bf g)\operatorname{-wtmod}$ is a vertex tensor categ…

Let $\mathscr{E}$ be the category formed by the $W^0_{\!A_2}(2)$-modules obtained by decomposing the $L_{-\frac{3}{2}}(\mathfrak{sl}_3)$-modules in $\mathscr{D}$. Let…

Let $\mathscr{D}$ be the category of weight $L_{-\frac{3}{2}}(\mathfrak{sl}_3)$-modules with finite-dimensional weight spaces and real weights. Let $\mathbin{\boxtimes}$ denote its…

Let $\mathscr{D}$ be the category of weight L_{-\frac{3}{2}(\mathfrak{sl}_3)-modules with finite-dimensional weight spaces and real weights, and let $\mathscr{C}_{\mathbb{R}}$ be…

Let $Y_{0,M,N}$ be a $Y$-algebra with one label equal to zero. The KL-category conjecture. The corresponding $Y_{0,M,N}$-algebra should have categories of type…

Let $m,n\geq2$, let $\psi$ be generic, and set $k=\psi-m+1$ and $\ell=\phi-n+1$, where $\phi^{-1}+\psi^{-1}=1$. Let $\mathcal H$ be a rank-one Heisenberg algebra. The D-algebra cat…