Kyoto Journal of Mathematics
- Kyoto J. Math.
- Volume 57, Number 2 (2017), 445-474.
Degenerate affine Grassmannians and loop quivers
We study the connection between the affine degenerate Grassmannians in type , quiver Grassmannians for one vertex loop quivers, and affine Schubert varieties. We give an explicit description of the degenerate affine Grassmannian of type and identify it with semi-infinite orbit closure of type . 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 , propose a conjectural description in the symplectic case, and discuss the generalization to the case of the affine degenerate flag varieties.
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
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
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]
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. https://projecteuclid.org/euclid.kjm/1494295226