张量范畴的正性猜想简史

IF 0.1 Q4 MATHEMATICS

Bulletin of the Institute of Mathematics Academia Sinica New Series Pub Date : 2017-03-27 DOI:10.21915/bimas.2019202

G. Mason

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引用次数: 3

摘要

我们证明了有限群的存在性 $G$ 不可简化的具有不可简化特征的 $\chi$ 用Frobenius-Schur指示器 $\nu_2(\chi){=}{+}1$ 这样 $\chi^2$ 有不可约的成分吗 $\varphi$ 有 $\nu_2(\varphi){=}{-}1$．这为有理CFT中的正性猜想和王正汉关于关键融合范畴的猜想提供了反例。

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A Brief History of the Positivity Conjecture in Tensor Category

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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来源期刊

Bulletin of the Institute of Mathematics Academia Sinica New Series MATHEMATICS-

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