On a necessary condition for unitary categorification of fusion rings
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.
9 pages, latex; the paper is updated with information that the first half of Question 5.8 has been answered (by other authors). Dedication to the memory of Earl J. Taft added