Quiver varieties and Beilinson-Drinfeld Grassmannians of type A

2007/12/26 by Ivan Mirković, Mirković, Ivan, Maxim Vybornov +1 · 3 citations
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.0712.4160

openalex publication_date 2007/12/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• A geometric Schur functor
• Lectures on Nakajima's Quiver Varieties
• Cyclic sieving, rotation, and geometric representation theory

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