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.

arXiv comment36 pages. Minor errors corrected on page 12, references added

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Cited by in corpus (19)

• Lectures on Nakajima's Quiver Varieties
• Yangians and quantizations of slices in the affine Grassmannian
• 2-block Springer fibers: convolution algebras and coherent sheaves
• An introduction to affine Grassmannians and the geometric Satake equivalence
• The Coulomb Branch of 3d $\mathcal{N}=4$ Theories
• Mirabolic affine Grassmannian and character sheaves
• The symplectic arc algebra is formal
• Diagram automorphisms of quiver varieties
• The Beilinson-Drinfeld Grassmannian and symplectic knot homology
• Beilinson-Drinfeld Schubert varieties and global Demazure modules
• Quantized Coulomb Branches, Monopole Bubbling and Wall-Crossing Phenomena in 3d $\mathcal{N}=4$ Theories
• A geometric Schur functor
• Quiver varieties and quantum Knizhnik--Zamolodchikov equation
• Geometric Satake, Springer correspondence, and small representations II
• Isomorphisms of quantizations via quantization of resolutions
• Cyclic sieving, rotation, and geometric representation theory
• Computing fusion products of MV cycles using the Mirkovic-Vybornov isomorphism
• Modular representations in type A with a two-row nilpotent central character
• Cotangent Bundles of Partial Flag Varieties and Conormal Varieties of their Schubert Divisors