2 problems

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 $\mathrm{SB}^{p|q}=\beta\gamma^{\otimes p}\otimes bc^{\otimes q}$,…