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Type a quiver loci and Schubert varieties
Journal article   Open access

Type a quiver loci and Schubert varieties

Ryan Kinser and Jenna Rajchgot
Journal of commutative algebra, Vol.7(2), pp.265-301
2015
DOI: 10.1216/JCA-2015-7-2-265
url
https://doi.org/10.1216/JCA-2015-7-2-265View
Published (Version of record) Open Access

Abstract

We describe a closed immersion from each representation space of a type $A$ quiver with bipartite (i.e., alternating) orientation to a certain opposite Schubert cell of a partial flag variety. This ``bipartite Zelevinsky map'' restricts to an isomorphism from each orbit closure to a Schubert variety intersected with the above-mentioned opposite Schubert cell. For type $A$ quivers of arbitrary orientation, we give the same result up to some factors of general linear groups.

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