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

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.

29 pages;Table 1 reproduced from arXiv:math/9812022 [math.QA]; v2 : no changes in main results, paper reorganized, introduction rewritten, notations polished, typos corrected, references added; v3 : typos corrected; v4 : minor changes

References in corpus (3)

• A cluster algebra approach to q-characters of Kirillov-Reshetikhin modules
• A Proof of the KNS conjecture : $D_r$ case
• Linear recurrence relations in $Q$-systems and difference $L$-operators

Cited by in corpus (2)

• Linear recurrence relations in $Q$-systems and difference $L$-operators
• Exponents Associated with $Y$-Systems and their Relationship with $q$-Series