Structure constants for pre-modular categories

2020/02/13 by Burciu, Sebastian
#FOS: Mathematics #Group Theory (math.GR) #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2002.05483

Abstract

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 a such 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 \citezz) in the settings of semisimple quasitriangular Hopf algebras.

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