10 problems

Let $\mathcal{FT}_k(\mathfrak{sl}_n)$ be the Feigin–Tipunin algebra, let ${\text{FF}}(nk)$ be the free-fermion VOA with $nk$ copies of free fermions, and let…

Let $k\geq1$, $a\in\{0,1\}$, and let $\eta$ be a partition with multiplicity vector $m(\eta)$. Level-rank configuration-sum conjecture. For the parameters appearing in the source,…

Let $Gr(n,k)$ denote the Grassmannian coset model with positive integers $n$ and $k$. Level-rank duality conjecture. The Grassmannian cosets should be invariant under exchanging…

Uglov's bijections describe the level-rank duality for affine type $A$. A categorical level-rank duality lifts these bijections to equivalences between representation-theoretic cat…

Level-rank duality conjecture. This map is an isomorphism. The source states that this conjecture was proven by Marian and Oprea and by Belkale, so it is recorded as solved.

Level-rank conjecture. The two image sets are unions of $H_{L,\lambda}^G(\zeta_m)$- and $H_{M,\mu}^G(\zeta_l)$-blocks, respectively; the bijection between them induced by…

Let the matching blocks be as in the intersection-of-series block bijection conjecture, and let $\vec{\nu}_e$ and $\vec{\nu}_m$ be charges for the corresponding specializations. Le…

Let $\mathbb{G}$ be a generic group, let $e,m>0$, and let $(\mathbb{L},\lambda)$ and $(\mathbb{M},\mu)$ be respectively $\Phi_e$- and $\Phi_m$-cuspidal pairs. Let the intersection…

Let $\widetilde{{\mathcal N}}_{n,k}$ be the slight modification of the boundary VOA ${\mathcal N}_{n,k}$ obtained by successive extension and orbifold, let…

Let $N$ and $M$ be the parameters of the level-rank duality, let $X$ be the partially ordered set defined by the relations in the source, and let $\mathcal{A}(X)$ be the set of all…