Finite -algebras of \(\mathfrak {osp}_{1|2n}\) and ghost centers

We prove that the finite -algebra \(U(\mathfrak {osp}_{1|2n}, f_\textrm{prin})\) $U({\mathfrak{osp}}_{1|2n},f_{\text{prin}})$ associated to \(\mathfrak {osp}_{1|2n}\) ${\mathfrak{osp}}_{1|2n}$ and its principal nilpotent element \(f_\textrm{prin}\) $f_{\text{prin}}$ is isomorphic to Gorelik’s ghost center of \(\mathfrak {osp}_{1|2n}\) ${\mathfrak{osp}}_{1|2n}$ . It is an analogue for \(\mathfrak {osp}_{1|2n}\) ${\mathfrak{osp}}_{1|2n}$ of a theorem of Kostant (Invent Math 48(2):101–184, 1978).