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arXiv · 1708.00560

Theta functions for lattices of SU(3) hyper-roots

Robert Coquereaux
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Abstract

We recall the definition of the hyper-roots that can be associated to modules-categories over the fusion categories defined by the choice of a simple Lie group G together with a positive integer k. This definition was proposed in 2000, using another language, by Adrian Ocneanu. If G=SU(2), the obtained hyper-roots coincide with the usual roots for ADE Dynkin diagrams. We consider the associated lattices when G=SU(3) and determine their theta functions in a number of cases; these functions can be expressed as modular forms twisted by appropriate Dirichlet characters.

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Robert Coquereaux. 2017-08-02. Theta functions for lattices of SU(3) hyper-roots. https://doi.org/10.1080/10586458.2018.1446062

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