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

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