8 problems

Let $\mathfrak g$ be a finite-dimensional simple Lie algebra and let $V^k(\mathfrak g)$ be the universal affine vertex algebra at level $k$, with simple graded quotient…

Let $\mathfrak{g}=\mathfrak{osp}_{m|2n}$, let $\widehat{\mathfrak{g}}$ be its affine Kac–Moody superalgebra, and let $\mathfrak{z}(\widehat{\mathfrak{g}})$ be the centre of the ass…

Let $\mathfrak{g}=\mathfrak{osp}_{M|2n}$, let $\widehat{\mathfrak{g}}$ be its affine Kac–Moody superalgebra, and let $\mathfrak{z}(\widehat{\mathfrak{g}})$ be the centre of the aff…

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…

Assume $m>1$ and set … Let $\mathcal H$ be a Heisenberg vertex algebra and $L_{\psi-m-1}(\mathfrak{sl}_m)$ the simple affine vertex algebra at level $\psi-m-1$. The coset embedding…

Let $V_k({\mathfrak s}{\mathfrak l}_2)$ be the universal affine vertex algebra associated to ${\mathfrak s}{\mathfrak l}_2$ at level $k$, with $SL(2)$ acting by the adjoint action.…