Irreducible components of two-row Springer fibers and Nakajima quiver varieties

2019/10/07 by Mee Seong Im, Im, Mee Seong, Chun‐Ju Lai +3 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1910.03010

openalex publication_date 2019/10/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give an explicit description of the irreducible components of two-row Springer fibers in type A as closed subvarieties in certain Nakajima quiver varieties in terms of quiver representations. By taking invariants under a variety automorphism, we obtain an explicit algebraic description of the irreducible components of two-row Springer fibers of classical type. As a consequence, we discover relations on isotropic flags that describe the irreducible components.

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Related

• Irreducible components of two-row Springer fibers for all classical types
• Reducibility of the intersections of components of a Springer fiber
• Quivers of type A, flag varieties and representation theory
• Irreducible components of two-column Δ-Springer fibers
• Intersections of components of a Springer fiber of codimension one for the two column case