3 problems

Let $L(\Lambda)$ be an integrable nonzero-level module over the affine Lie superalgebra in the surrounding section, with $\Lambda\in\Omega_k$ or $\Lambda\in\Omega'_k$. Define…

Let $\mathbb F_q$ be a fixed finite field, let $U_n$ be the group of unipotent upper-triangular matrices over $\mathbb F_q$, let $G_n=GL_n(\mathbb F_q)$, and let $\chi$ be a superc…

Kac–Wakimoto's conjecture. There exists $b\in\mathbb{Q}$ such that the supercharacter of $V$ is divisible by the $b$-th power of the supercharacter of the trivial module, with $b$…