Finite $\mathcal{W}$-algebras of ${\mathfrak{osp}}_{1|2n}$ and Ghost centers

Abstract

We prove that the finite $\mathcal{W}$-algebra associated to ${\mathfrak{osp}}_{1|2n}$ and its principal nilpotent element is isomorphic to Gorelik's ghost center of ${\mathfrak{osp}}_{1|2n}$, which proves an analog of Kostant's theorem for ${\mathfrak{osp}}_{1|2n}$.

14 pages