Theta-null values are characterized as the unique solutions of a manifestly modular-invariant system of differential equations of infinite order built from the supersymmetry algebra osp(1|2n).
Strongly typical representations of the basic classical Lie superalgebras
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abstract
The category of representations with a strongly typical central character of a basic classical Lie superalgebra is proven to be equivalent to the category of representations of its even part corresponding to an appropriate central character. For a Lie superalgebra $osp(1,2l)$ the category of representations with a "generic" weakly atypical central character is described.
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Supersymmetry, differential operators of infinite order and theta functions
Theta-null values are characterized as the unique solutions of a manifestly modular-invariant system of differential equations of infinite order built from the supersymmetry algebra osp(1|2n).