Conjugacy classes and centralizers for pivotal fusion categories

Abstract

A criterion for Müger centralizer of a fusion subcategory of a braided non-degenerate fusion category is given. Along the way we extend some identities on the space of class functions of a fusion category introduced by Shimizu in \cite{scalg}. We also show that in a modular tensor category the product of two conjugacy class sums is a linear combination of conjugacy class sums with rational coefficients.

34 pp. arXiv admin note: text overlap with arXiv:1504.01178 by other authors