Quiver varieties and Beilinson-Drinfeld Grassmannians of type A

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.

36 pages. Minor errors corrected on page 12, references added

References in corpus (1)

• Relation between two geometrically defined bases in representations of $G{L}_n$

Cited by in corpus (2)

• Lectures on Nakajima's Quiver Varieties
• The Beilinson-Drinfeld Grassmannian and symplectic knot homology