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arXiv · 1410.0777

Degenerate affine Grassmannians and loop quivers

Evgeny Feigin·Michael Finkelberg·Markus Reineke
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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 $GL_n$ 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.

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Evgeny Feigin, Michael Finkelberg, Markus Reineke. 2014-10-03. Degenerate affine Grassmannians and loop quivers. https://doi.org/10.1215/21562261-3821864

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