A Brief History of the Positivity Conjecture in Tensor Category
by Geoffrey Mason  

Vol. 14 No. 2 (2019) P.149~P.153

DOI:	https://doi.org/10.21915/BIMAS.2019202
	10.21915/BIMAS.2019202

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 $\varphi$ with $\nu_2(\varphi){=}{-}1$. This provides counterexamples to the positivity conjecture in rational CFT and a conjecture of Zhenghan Wang about pivotal fusion categories.

KEYWORDS
Fusion category, positivity conjecture, Frobenius-Schur indicator.

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 18D10,20G05

MILESTONES

Received: 2017-06-18
Revised : 2018-04-01
Accepted: 2018-04-09

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