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

24 pages

Cited by in corpus (2)

• Non-split supermanifolds associated with the cotangent bundle
• Vector fields on ${\mathfrak{osp}}_{2m-1|2n}(\mathbb{C})$-flag supermanifolds