8 problems

Let $L(\Lambda)$ be a highest weight module with highest weight $\Lambda$. A highest weight module $L(\Lambda)$ is modular invariant when its character has the relevant modular-inv…

Coset $W_N$-generation conjecture. For a more general affine Lie superalgebra, the coset space

Singular-vector isospin conjecture. The singular vectors in the admissible representations are conjectured to be precisely those with isospin satisfying the displayed relation. Thi…

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…

Let $\widehat{\mathfrak{g}}$ be an affine Kac–Moody Lie superalgebra obtained from a basic classical Lie superalgebra by adjoining the degree derivation. Consider the family of bou…

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 $\chi_{M,N}$…

For every even integer $n\geq 0$, let $V_{-2}(\mathfrak{osp}(n+8\mid n))$ be the associated affine vertex superalgebra, and let $V_{-2}(\mathfrak{so}(8))$ be the affine vertex alge…