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.

中文翻译：

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D 型箭袋表示变体、双格拉斯曼变体和对称变体

我们统一了$D$ quiver 表示变体、双Grassmannians 和对称变体$GL(a+b)/GL(a)\times GL(b)$ 等变几何的各个方面；特别是，我们翻译了关于轨道闭合奇点、轨道闭合遏制组合学以及这三个系列之间的环面等变 $K$ 理论的结果。这些结果都是从我们将 Zelevinsky 构造的 $A$ quivers 类型推广到 $D$ 类型设置中获得的。更准确地说，我们将具有良好特性的同质纤维束在类型 $D$ quiver 表示变体上的显式嵌入到这些对称变体中。