In this paper, we study conjugacy classes for pivotal fusion categories. In particular, we prove a Burnside type formula for the structure constants concerning the product of two conjugacy class sums of such a fusion category. For a braided weakly integral fusion category $\mathcal{C}$, we show that these structure constants multiplied by $dim(\mathcal{C})$ are non-negative integers, extending some results obtained by Zhou and Zhu (see Preprint, 2019, arXiv:1912.07831v1) in the settings of semisimple quasitriangular Hopf algebras.

中文翻译：

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预模块类别的结构常数

在本文中，我们研究了关键融合类别的共轭类。特别是，我们证明了关于这种融合类别的两个共轭类和的乘积的结构常数的 Burnside 型公式。对于编织弱积分融合类别$\mathcal{C}$，我们表明这些结构常数乘以 $暗淡(\mathcal{C})$ 是非负整数，扩展了 Zhou 和 Zhu（参见 Preprint，2019，arXiv:1912.07831v1）在半简单拟三角 Hopf 代数设置中获得的一些结果。