Nilpotent orbits and Hilbert schemes

2007/01/31 by Craig Jackson, Craig M. Jackson, Jackson, Craig
Mathematics · #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG) #math.GT #math.SG

paper · pdf · doi:10.48550/arxiv.math/0701909

arxiv created 2007/01/31 · openalex publication_date 2007/01/31 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct embeddings Y_n,τ → Hilbⁿ (Σ_τ) for each of the classical Lie algebras \gersp_2m(\Cc), \gerso_2m(\Cc), and \gerso_2m+1(\Cc). The space Y_n,τ is the fiber over a point τ∈ \ger h / W of the restriction of the adjoint quotient map χ: \ger g → \ger h /W to a suitably chosen transverse slice of a nilpotent orbit. These embeddings were discovered for \gersl_2m(\Cc) by Ciprian Manolescu. They are related to the symplectic link homology of Seidel and Smith.

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