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

Robert Coquereaux (1, 2)

1 CPT - Centre de Physique Théorique - UMR 7332
2 CPT - E2 Géométrie, Physique et Symétries

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.

Domaines: Algèbres quantiques [math.QA]; Physique mathématique [math-ph]; Théorie des représentations [math.RT]; Théorie des groupes [math.GR]

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⟩