8 problems

Coset conjecture. The commutant $\operatorname{Com}(W,V)$ is also rational and lisse. This is presented as a widely believed assertion and is used in the paper to deduce rationalit…

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 $\mathfrak{g}$ be a reductive simply-laced Lie algebra, let $n$ be a positive integer, and let $P^+_n$ be the set of dominant integral weights of $\mathfrak{g}$ such that…

Let $n,m$ be positive integers and let $p$ satisfy … Let $\mathcal{W}_{n,m}$ be the family of W-algebras defined by quantum Hamiltonian reduction, let…

Type A coset conjecture. There is an isomorphism

Type C coset conjecture. The vertex algebra ${\mathcal C}_k(n)$ is isomorphic to the $C_2$-cofinite, rational principal ${\mathcal W}$-algebra…

Let $k$ be a positive integer. The affine algebra $L_k({\mathfrak{sl}}_2)$ is expected to be a sub-VOA of $L_k({\mathfrak{osp}}(1|2))$. Affine osp(1|2) rationality conjecture. The…

For general $n$, let $W^{(2)}_n$ be the Feigin–Semikhatov algebra at level $k=-n^2/(n+1)$, let $\mathcal B_{n+1}$ be the subalgebra constructed in the $(1,n+1)$-theory, and let…