  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.
