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arXiv · 1901.10014

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

Ryan Kinser·Jenna Rajchgot
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Abstract

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.

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Ryan Kinser, Jenna Rajchgot. 2019-01-28. Type D quiver representation varieties, double Grassmannians, and symmetric varieties. https://arxiv.org/abs/1901.10014

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