• A
  • A
  • A
  • ABC
  • ABC
  • ABC
  • А
  • А
  • А
  • А
  • А
Regular version of the site

Working paper

Degenerate affine Grassmannians and loop quivers

arxiv.org. math. Cornell University, 2014. No. 1410.0777.
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 $GL_n$ 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 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.