Degenerate affine Grassmannians and loop quivers

Abstract

We study the connection between the affine degenerate Grassmannians in type $A$, quiver Grassmannians for one vertex loop quivers and affine Schubert varieties. We give an explicit description of the degenerate affine Grassmannian of type $G{L}_n$ 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 type $A_1^{(1)}$, propose a conjectural description in the symplectic case and discuss the generalization to the case of the affine degenerate flag varieties.

27 pages

References in corpus (3)

• Quiver Grassmannians and degenerate flag varieties
• Local models of Shimura varieties, I. Geometry and combinatorics
• Symplectic degenerate flag varieties

Cited by in corpus (1)

• Desingularizations of Quiver Grassmannians for the Equioriented Cycle Quiver