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.Comment: 33 pages, 9 figure
