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

TL;DR

This paper establishes an isomorphism between finite W-algebras of osp_{1|2n} and Gorelik's ghost center, extending Kostant's theorem to this superalgebra context.

Contribution

It proves a new isomorphism linking finite W-algebras and ghost centers for osp_{1|2n}, providing a superalgebra analog of Kostant's theorem.

Findings

Finite W-algebra of osp_{1|2n} is isomorphic to Gorelik's ghost center.

Extends Kostant's theorem to the superalgebra osp_{1|2n}.

Provides new structural insights into the representation theory of osp_{1|2n}.

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 $\mathfrak{osp}_{1|2n}$.