Semisimple Super Tannakian Categories with a small Tensor Generator

Abstract

We consider semisimple super Tannakian categories generated by an object whose symmetric or alternating tensor square is simple up to trivial summands. Using representation theory, we provide a criterion to identify the corresponding Tannaka super groups that applies in many situations. As an example we discuss the tensor category generated by the convolution powers of an algebraic curve inside its Jacobian variety.

References in corpus (7)

• Vanishing Theorems for constructible Sheaves on Abelian Varieties
• Perverse sheaves on semiabelian varieties
• Semisimple algebraic tensor categories
• Brill-Noether Sheaves
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• Why certain Tannaka groups attached to abelian varieties are almost connected
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Cited by in corpus (5)

• Cubic threefolds, Fano surfaces and the monodromy of the Gauss map
• Characteristic cycles and the microlocal geometry of the Gauss map, II
• On classical tensor categories attached to the irreducible representations of the General Linear Supergroups $GL(n|n)$
• Summands of theta divisors on Jacobians
• Arithmetic Fourier transforms over finite fields: generic vanishing, convolution, and equidistribution