6 problems

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 $\mathsf{k}$ be admissible-nondegenerate. For $\ell,\ell'\in\mathbb{Z}$, $[j],[j']\in\mathbb{R}/\mathbb{Z}$, and…

Verlinde-coefficient conjecture. The Verlinde coefficient $N^{\mu_2}_{\lambda,\mu_1}$ can be expressed as a certain delta function with a non-negative integer coefficient, and this…

Let $p\in\mathbb{Z}_{\ge 2}$. For $j\in\mathbb{Z}$, let $\pi_j$ be the irreducible $\overline{M(1)}$-module defined in the surrounding construction, and let $M_t$ denote the corres…

Simple multiplicity conjecture. The fusion rules of $\mathfrak W_{n,\ell}$ are

Let $A$ be a free quantum algebra, meaning a Hopf algebra satisfying … whose tensor category is spanned by partitions. Let $R^+(A)$ denote its fusion semiring. Freeness conjecture.…