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 G L ( a + b ) / G L ( a ) × G L ( 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.