A brief history of the positivity conjecture in tensor category theory

Abstract

We show the existence of a finite group $G$ having an irreducible character $\chi$ with Frobenius-Schur indicator ${\nu }_2(\chi )=+1$ such that ${\chi }^2$ has an irreducible constituent $\phi$ with ${\nu }_2(\phi )=-1$. This provides counterexamples to the positivity conjecture in rational CFT and a conjecture of Zhenghan Wang about pivotal fusion categories.

This is version includes needed corrections pointed out by an Arxiv editor. I have no idea how to get a local report number!

References in corpus (1)

• A reason for fusion rules to be even