Schubert varieties for the super affine Grassmannian of $GL_{n|m}$

Abstract

We study Schubert varieties of the affine Grassmannian for the general linear supergroup $GL_{n|m}$. An explicit computational study is conducted in low-dimensional cases, namely for dimensions $n|m = 1|1$ and $2|1$. We describe the supervariety structures that arise in these settings, providing coordinate descriptions, equations, and morphisms.