2 problems

Let $\mathfrak{g}$ be a simple Lie algebra, $f$ a nilpotent element, and $k$ an admissible level. Let $\mathbb{O}_k$ denote the corresponding nilpotent orbit. Rationality conjectur…

Let $N\in\mathbb{Z}_{>0}$ and let $k=-N+p/n$ be admissible. Write $\pi$ for a rank-one Heisenberg vertex algebra, and set $L_\bullet(\mathfrak{sl}_i)=\mathbb{C}$ for $i=0,1$. Excep…