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Modularity and tensor categories for affine vertex algebras at admissible level Creutzig, Thomas


A well-known result is that modules of a rational vertex algebra form a modular tensor category and that the modular group action on graded traces coincides with the categorical one. Prime examples are affine vertex algebras at positive integer level.  I would like to explain the state of the art for affine vertex algebras at admissible level and our knowledge is mainly restricted to the case of sl(2). From the character point of view three types of traces arise: vector-valued modular forms, meromorphic Jacobi forms and formal distributions. There are also three types of categories one can associate to the affine vertex algebra and categorical action of the modular group seems to coincide with the one on characters. 

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