Vector fields on $\mathfrak{osp}_{2m-1|2n}(\mathbb C)$-flag supermanifolds

TL;DR

This paper computes the Lie superalgebras of holomorphic vector fields on specific isotropic flag supermanifolds associated with the orthosymplectic Lie superalgebra, advancing understanding of their geometric and algebraic structures.

Contribution

It provides explicit calculations of the Lie superalgebras of holomorphic vector fields on maximal isotropic flag supermanifolds related to rak{osp}_{2m-1|2n}(\u00a0C), a novel contribution to supergeometry.

Findings

Explicit Lie superalgebra structures obtained

Classification of vector fields on these supermanifolds

Enhanced understanding of supermanifold symmetries

Abstract

We compute the Lie superalgebras of holomorphic vector fields on isotropic flag supermanifolds of maximal type corresponding to the Lie superalgebra $\mathfrak{osp}_{2m-1|2n}(\mathbb C)$.