Junhwi Lim
Australian National University
Title
An Analytic Obstruction to Unitary Categorification of Fusion Rings
Abstract
The construction of unitary tensor categories and subfactors typically requires solving large systems of equations, namely the pentagon and biunitary equations. These equations arise from based rings (in particular, fusion rings) and inclusion matrices. There is no known systematic method for solving them, and in many cases no solution exists. We introduce an a priori criterion for excluding such cases without having to solve the equations. The criterion is based on a noncommutative analogue of the Minkowski integral inequality.
