Structure constants for premodular categories

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 C, we show that these structure constants multiplied by dim(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.

Automated summary

This paper studies conjugacy classes for pivotal fusion categories and proves a Burnside type formula for the structure constants concerning the product of two conjugacy class sums of such a fusion category. It also shows that for a braided weakly integral fusion category, these structure constants multiplied by dim(C) are non-negative integers, expanding on previous results in the settings of semisimple quasitriangular Hopf algebras by Zhou and Zhu.