Kyoto Journal of Mathematics

Degenerate affine Grassmannians and loop quivers

Evgeny Feigin, Michael Finkelberg, and Markus Reineke

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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 GLn and identify it with semi-infinite orbit closure of type A2n1. We show that principal quiver Grassmannians for the one vertex loop quiver provide finite-dimensional appro- ximations of the degenerate affine Grassmannian. Finally, we give an explicit description of the degenerate affine Grassmannian of type A1(1), propose a conjectural description in the symplectic case, and discuss the generalization to the case of the affine degenerate flag varieties.

Article information

Kyoto J. Math., Volume 57, Number 2 (2017), 445-474.

Received: 30 September 2015
Revised: 26 November 2015
Accepted: 31 March 2016
First available in Project Euclid: 9 May 2017

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Zentralblatt MATH identifier

Primary: 17B67: Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras
Secondary: 16G20: Representations of quivers and partially ordered sets 14M15: Grassmannians, Schubert varieties, flag manifolds [See also 32M10, 51M35]

affine Kac–Moody algebras quiver Grassmannians flag varieties


Feigin, Evgeny; Finkelberg, Michael; Reineke, Markus. Degenerate affine Grassmannians and loop quivers. Kyoto J. Math. 57 (2017), no. 2, 445--474. doi:10.1215/21562261-3821864.

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