On quiver varieties and affine Grassmannians of type A

Details On quiver varieties and affine Grassmannians of type A On quiver varieties and affine Grassmannians of type A

2002-06-09

arxiv.org/abs/math/0206084v2

Mathematics

Algebraic Geometry

5 pages, section 3.3 added

Scientific paper

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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