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arXiv · 1412.3884

Three-term recurrence relations of minimal affinizations of type $G_2$

Li Qiao·Jian-Rong Li
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Abstract

Minimal affinizations form a class of modules of quantum affine algebras introduced by Chari. We introduce a system of equations satisfied by the $q$-characters of minimal affinizations of type $G_2$ which we call the M-system of type $G_2$. The M-system of type $G_2$ contains all minimal affinizations of type $G_2$ and only contains minimal affinizations. The equations in the M-system of type $G_2$ are three-term recurrence relations. The M-system of type $G_2$ is much simpler than the extended T-system of type $G_2$ obtained by Mukhin and the second author. We also interpret the three-term recurrence relations in the M-system of type $G_2$ as exchange relations in a cluster algebra constructed by Hernandez and Leclerc.

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BibTeXRIS

Li Qiao, Jian-Rong Li. 2014-12-12. Three-term recurrence relations of minimal affinizations of type $G_2$. https://arxiv.org/abs/1412.3884

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