6 problems

Let $\mathcal{W}^k(\mathfrak{sl}_n,f_{\mathrm{sub}})$ be the subregular $\mathcal{W}$-algebra of $\mathfrak{sl}_n$, where $f_{\mathrm{sub}}$ is in the nilpotent orbit corresponding…

Let $V^k(\mathfrak{sl}_{n+1})$ be the universal affine vertex algebra of $\mathfrak{sl}_{n+1}$ at level $k$, let $bc^{\otimes n}$ be the tensor product of $n$ copies of the $bc$-sy…

Let a shifted affine super Yangian be a modification of the affine super Yangian adapted to the non-rectangular setting, and let a type $A$ $W$-superalgebra be the corresponding…

Let $N,n,m\in\mathbb{Z}$ satisfy $N>n,m\geq2$, and define $k^\sharp=-k-N+n+m$ and $\ell^\sharp=-\ell-N+n+m$. Let $\operatorname{Com}(A,B)$ denote the commutant of $A$ in $B$. Verti…

Let $n,r\geq0$, let $\mathcal{W}^k(\mathfrak{sl}_{n+r|n},f_{n+r|n})$ be the universal regular W-superalgebra, let $\mathrm{SB}^{p|q}=\beta\gamma^{\otimes p}\otimes bc^{\otimes q}$,…

Strong rationality conjecture. The principal ${\mathcal W}$-superalgebra ${\mathcal W}_{\ell}({\mathfrak o}{\mathfrak s}{\mathfrak p}_{2n|2n})$ is strongly rational.