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arXiv · 1302.1467

Positivity and periodicity of $Q$-systems in the WZW fusion ring

Chul-hee Lee
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Abstract

We study properties of solutions of $Q$-systems in the WZW fusion ring obtained by the Kirillov-Reshetikhin modules. We make a conjecture about their positivity and periodicity and give a proof of it in some cases. We also construct a positive solution of the level $k$ restricted $Q$-system of classical types in the fusion rings. As an application, we prove some conjectures of Kirillov and Kuniba-Nakanishi-Suzuki on the level $k$ restricted $Q$-systems.

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Chul-hee Lee. 2013-02-06. Positivity and periodicity of $Q$-systems in the WZW fusion ring. https://doi.org/10.1016/j.aim.2017.02.031

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