Type D quiver representation varieties, double Grassmannians, and symmetric varieties

We unify aspects of the equivariant geometry of type D quiver representation varieties, double Grassmannians, and symmetric varieties GL(a + b)/GL(a) x GL(b); in particular we translate results about singularities of orbit closures, combinatorics of orbit closure containment, and torus equivariant K-theory between these three families. These results are all obtained from our generalization of a construction of Zelevinsky for type A quivers to the type D setting. More precisely, we give explicit embeddings with nice properties of homogeneous fiber bundles over type D quiver representation varieties into these symmetric varieties. (c) 2020 Elsevier Inc. All rights reserved.

Automated summary

This paper unifies the equivariant geometry of type D quiver representation varieties, double Grassmannians, and symmetric varieties GL(a + b)/GL(a) x GL(b), by translating results about singularities of orbit closures, combinatorics of orbit closure containment, and torus equivariant K-theory between these three families. These results are all obtained from a generalization of Zelevinsky's construction for type A quivers to the type D setting, by giving explicit embeddings with nice properties of homogeneous fiber bundles over type D quiver representation varieties into these symmetric varieties.