Vector fields on \mathfrakgl_m|n(\mathbb C)-flag supermanifolds

2015/09/14 by Elizaveta Vishnyakova, Vishnyakova, Elizaveta
Mathematics · #Advanced Topics in Algebra #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1509.04047

openalex publication_date 2015/09/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The main result of this paper is the computation of the Lie superalgebras of holomorphic vector fields on complex flag supermanifolds, introduced by Yu.I.Manin. We prove that with several exceptions any holomorphic vector field is fundamental with respect to the natural action of the Lie superalgebra \mathfrak gl_m|n(\mathbb C).

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