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arXiv · 0712.4160

Quiver varieties and Beilinson-Drinfeld Grassmannians of type A

Ivan Mirković·Maxim Vybornov
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Abstract

We construct Nakajima's quiver varieties of type A in terms of conjugacy classes of matrices and (non-Slodowy's) transverse slices naturally arising from affine Grassmannians. In full generality quiver varieties are embedded into Beilinson-Drinfeld Grassmannians of type A. Our construction provides a compactification of Nakajima's quiver varieties and a decomposition of an affine Grassmannian into a disjoint union of quiver varieties. As an application we provide a geometric version of skew and symmetric $(GL(m), GL(n))$ duality.

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Ivan Mirković, Maxim Vybornov. 2008-12-30. Quiver varieties and Beilinson-Drinfeld Grassmannians of type A. https://arxiv.org/abs/0712.4160

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