Vector fields on Π-symmetric flag supermanifolds

2015/06/07 by Vishnyakova, E. G.
#Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1506.02295

Abstract

The main result of this paper is the computation of the Lie superalgebras of holomorphic vector fields on the complex Π-symmetric flag supermanifolds, introduced by Yu.I.~Manin. We prove that with one exception any vector field is fundamental with respect to the natural action of the Lie superalgebra \mathfrak q_n(\mathbb C).

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