6 problems

Let $L_k(\mathfrak{sl}_N)$ be the simple affine vertex algebra at level $k$, let $f_\lambda$ be the nilpotent indexed by a partition $\lambda\vdash N$, and let $H_{f_\lambda}$ deno…

Let $\mathcal{W}^{\mathfrak{sp}}_{\infty}(c,\mathsf{k})$ be the universal two-parameter vertex algebra, let $\mathrm{H}^0_{\ydiagram{2}}$ denote its Virasoro-type reduction, and le…

Let $\mathbb{O}$ be a nilpotent orbit of $\mathfrak{g}$, with representative $f\in\mathfrak{g}$ satisfying … and assume that the nonzero semisimple element of…

Let $\mathfrak{g}$ be $\mathfrak{so}_N$ or $\mathfrak{sp}_N$, and let … be a partition parametrizing a nilpotent orbit, with $m_i\in\{1,2\}$ subject to the parity conditions for th…

Let $\lambda=(\lambda_1\geq\lambda_2\geq\cdots\geq\lambda_\ell)$ be a partition of $N$, and set … Let $\mathrm{H}_{\mathbb{O}_{\widehat{\lambda}_i}}^0$ denote the BRST reduction as…

Let a family of physically motivated BRST reductions of beta-gamma systems and free fermions be given, and let $L_1(\mathfrak{psl}_{n|n})$ denote the simple level-one vertex algebr…