A brief history of the positivity conjecture in tensor category theory

Geoffrey Mason

A brief history of the positivity conjecture in tensor category theory

Quantum Algebra 2017-03-28 v1

Authors: Geoffrey Mason

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

positivity conjecture tensor category theory Frobenius-Schur indicator finite groups irreducible characters pivotal fusion categories rational conformal field theory

Cite

@article{arxiv.1703.08890,
  title  = {A brief history of the positivity conjecture in tensor category theory},
  author = {Geoffrey Mason},
  journal= {arXiv preprint arXiv:1703.08890},
  year   = {2017}
}

Comments

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

A brief history of the positivity conjecture in tensor category theory

Abstract

Keywords

Cite

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