Vector fields on $\mathfrak{osp}_{2m|2n}(\mathbb C)$- and $\pi\mathfrak{sp}_{n}(\mathbb C)$-flag supermanifolds

TL;DR

This paper computes the Lie superalgebras of holomorphic vector fields on certain isotropic flag supermanifolds, showing that under specific conditions, all such vector fields are generated by the natural Lie superalgebra actions.

Contribution

It provides a detailed computation of vector fields on isotropic flag supermanifolds related to specific Lie superalgebras, establishing their fundamental nature.

Findings

Holomorphic vector fields are fundamental under certain restrictions.

The structure of vector fields aligns with the natural Lie superalgebra actions.

Results apply to maximal type isotropic flag supermanifolds.

Abstract

The paper is devoted to a computation of the Lie superalgebras of holomorphic vector fields on isotropic flag supermanifolds of maximal type corresponding to the Lie superalgebras $\mathfrak{osp}_{2m|2n}(\mathbb C)$ and $\pi\mathfrak{sp}_{n}(\mathbb C)$. The result is that under some restrictions on the flag type any holomorphic vector field is fundamental with respect to the natural action of the Lie superalgebras $\mathfrak{osp}_{2m|2n}(\mathbb C)$ or $\pi\mathfrak{sp}_{n}(\mathbb C)$.