Monadicity of localization for Lie super-algebras \mathfrakgl(m, n)

2021/10/02 by Slava Pimenov, Pimenov, Slava
Mathematics · #14A30 #17B10 (Primary) #18G80 (Secondary) #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2110.00802

openalex publication_date 2021/10/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the localization functor from the category of representation of Lie super-algebra \mathfrakg = \mathfrakgl(m, n) into monodromic D-modules on the flag manifold X = G/B. We show that the right localization is monadic in a suitable sense, which identifies the coderived category of \mathfrakg-modules with the ind-completion of compactly generated W-modules for some algebra W in monodromic D_X-bimodules.

Citations

• Beilinson-Bernstein localization over the Harish-Chandra center
• Two kinds of derived categories, Koszul duality, and comodule-contramodule correspondence

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• On Singular Localization of \mathfrakg-modules
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