6 problems

Boundary-level rationality conjecture. The vertex operator superalgebra $L_{\widehat{\mathfrak{g}}}(\mathcal{k},0)$ is rational in the category $\mathcal{O}$, and its irreducible w…

Semisimplicity conjecture. The category $KL_k$ is semisimple if and only if

Let $\mathfrak{g}$ be the basic classical Lie superalgebra, let $L(\mathfrak{g})$ be its loop superalgebra, and let $\widehat{\mathfrak{g}}$ be the corresponding affine Lie superal…

Assume $N>M$ and let $c\neq0$ be a non-rational number. Let $\Gr_{\GL_N}$ denote the affine Grassmannian, $U_{M,N}(\bF)$ the relevant unipotent subgroup with character $\chi_{M,N}$…

Let $\widehat{\mathfrak{g}}$ be an affine Lie superalgebra, let $\varphi:\widehat{\mathfrak{g}}\to\widehat{\mathfrak{g}}$ be a compatible homomorphism, and let…

Let $\widehat{\mathfrak{g}}$ be an affine Lie superalgebra, let $L(\Lambda)$ be a partially integrable tame $\widehat{\mathfrak{g}}$-module, and let $L^\#$ be the relevant lattice…