On a necessary condition for unitary categorification of fusion rings

2021/02/26 by Etingof, Pavel, Nikshych, Dmitri, Ostrik, Victor
#FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.2102.13239

Abstract

In arXiv:1910.12059 Liu, Palcoux and Wu proved a remarkable necessary condition for a fusion ring to admit a unitary categorification, by constructing invariants of the fusion ring that have to be positive if it is unitarily categorifiable. The main goal of this note is to provide a somewhat more direct proof of this result. In the last subsection we discuss integrality properties of the Liu-Palcoux-Wu invariants.

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