  We unify aspects of the equivariant geometry of type $D$ quiver
representation varieties, double Grassmannians, and symmetric varieties
$GL(a+b)/GL(a)\times GL(b)$; 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.
