Article Dans Une Revue Experimental Mathematics Année : 2020

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

Résumé

We recall the definition of the hyper-roots that can be associated to modules-categories over 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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hal-01571963 , version 1 (20-04-2018)

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Robert Coquereaux. Theta functions for lattices of SU(3) hyper-roots. Experimental Mathematics, 2020, 29 (2), pp.137-162. ⟨10.1080/10586458.2018.1446062⟩. ⟨hal-01571963⟩
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