On The Construction Of Supergrassmannians As Homogeneous Superspaces

In this paper, we give an explicit description of the action of the super Lie group GL(m vertical bar n) on supergrassmannian G(k vertical bar l)(m vertical bar n) 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.