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On quiver varieties and affine 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 affine Grassmannians of type A. This gives a compactification of quiver varieties and a decomposition of affine Grassmannians into a disjoint union of quiver varieties. Consequently, singularities of quiver varieties, nilpotent orbits and affine Grassmannians are the same in type A. The construction also provides a geometric framework for skew $(GL(m), GL(n))$ duality and identifies the natural basis of weight spaces in Nakajima's construction with the natural basis of multiplicity spaces in tensor products which arises from affine Grassmannians.

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BibTeXRIS

Ivan Mirković, Maxim Vybornov. 2002-06-25. On quiver varieties and affine Grassmannians of type A. https://arxiv.org/abs/math/0206084

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