On the Construction of ${\mathbb{Z}}_2^n-$Supergrassmannians as Homogeneous ${\mathbb{Z}}_2^n-$Superspaces

Abstract

In this paper, we construct the ${\mathbb{Z}}_2^n-$supergrassmannians by gluing of the ${\mathbb{Z}}_2^n-$superdomains and give an explicit description of the action of the ${\mathbb{Z}}_2^n-$super Lie group $GL(\overrightarrow{\text{m}})$ on the ${\mathbb{Z}}_2^n-$supergrassmannian $G_{\overrightarrow{\text{k}}}(\overrightarrow{\text{m}})$ in the functor of points language. In particular, we give a concrete proof of the transitively of this action, and the gluing of the local charts of the supergrassmannian.

16 pages. arXiv admin note: substantial text overlap with arXiv:1801.02159

References in corpus (2)

• ${\mathbb{Z}}_2^n$-Supergeometry I: Manifolds and Morphisms
• Supergrassmannians as Homogeneous Superspaces