Degenerate affine Grassmannians and loop quivers

We study the connection between the affine degenerate Grassmannians in type A, quiverGrassmannians for one vertex loop quivers, and affine Schubert varieties. We give an explicit description of the degenerate affine Grassmannian of type GL_n and identify it with semi-infinite orbit closure of type A_2n-1.We show that principal quiver Grassmannians for the one vertex loop quiver provide finite-dimensional approximations of the degenerate affine Grassmannian. Finally, we give an explicit description of the degenerate affine Grassmannian of typeA⁽¹⁾₁, propose a conjectural description in the symplectic case, and discuss the generalization to the case of the affine degenerate flag varieties.