Degenerate affine Grassmannians and loop quivers

Evgeny Feigin, Michael Finkelberg, Markus Reineke

Research output: Contribution to journalArticlepeer-review

Abstract

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 GLn and identify it with semi-infinite orbit closure of type A2n-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.

Original languageEnglish
Pages (from-to)445-474
Number of pages30
JournalKyoto Journal of Mathematics
Volume57
Issue number2
DOIs
StatePublished - Jun 2017
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Mathematics

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