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arXiv · 1703.08890

A brief history of the positivity conjecture in tensor category theory

Geoffrey Mason
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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.

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Geoffrey Mason. 2017-03-27. A brief history of the positivity conjecture in tensor category theory. https://arxiv.org/abs/1703.08890

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