3 problems

Let $\fg$ be simple of simply-laced type, let $k\in\BQ$ satisfy $k+\check{\operatorname{\mathbbm{h}}}=m/u$ in lowest terms with $m\geq1$ and $\operatorname{gcd}(m,u)=1$, and let…

Let $\fg$ be simple of simply-laced type and let $k\in\BQ$ satisfy $k+\check{\operatorname{\mathbbm{h}}}=m/u$ in lowest terms with $m\geq1$. Let $\check{\fg}^{(u)}$ be the metaplec…

Let $\fg$ be a simple simply-laced Lie algebra, let $k\in\BQ$ satisfy $k+\check{\operatorname{\mathbbm{h}}}=m\geq1$, and let $L_k(\fg)$ be the simple affine vertex algebra. Let…