ABSTRACT We recall the definition of the hyper-roots that can be associated with 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.

中文翻译：

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SU(3) 超根点阵的 Theta 函数

摘要 我们回顾了超根的定义，它可以与模块类别相关联，而融合类别是通过选择一个简单的李群 G 和一个正整数 k 来定义的。这个定义是在 2000 年由 Adrian Ocneanu 使用另一种语言提出的。如果 G = SU(2)，则获得的超根与 ADE Dynkin 图的通常根一致。当 G = SU(3) 时，我们考虑相关的格子，并在许多情况下确定它们的 theta 函数；这些函数可以表示为由适当的狄利克雷字符扭曲的模块化形式。