Vector fields on $\mathfrak{gl}_{m|n}(\mathbb C)$ -flag supermanifolds

preprint2015arXivOpen access

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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Vector fields on $\mathfrak{gl}_{m|n}(\mathbb C)$ -flag supermanifolds

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Vector fields on glm∣n(C)\mathfrak{gl}_{m|n}(\mathbb C)glm∣n​(C)-flag supermanifolds

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Vector fields on $\mathfrak{gl}_{m|n}(\mathbb C)$ -flag supermanifolds