Three-term recurrence relations of minimal affinizations of type $G_2$
Abstract
Minimal affinizations form a class of modules of quantum affine algebras introduced by Chari. We introduce a system of equations satisfied by the -characters of minimal affinizations of type which we call the M-system of type . The M-system of type contains all minimal affinizations of type and only contains minimal affinizations. The equations in the M-system of type are three-term recurrence relations. The M-system of type is much simpler than the extended T-system of type obtained by Mukhin and the second author. We also interpret the three-term recurrence relations in the M-system of type as exchange relations in a cluster algebra constructed by Hernandez and Leclerc.
Keywords
Cite
@article{arxiv.1412.3884,
title = {Three-term recurrence relations of minimal affinizations of type $G_2$},
author = {Li Qiao and Jian-Rong Li},
journal= {arXiv preprint arXiv:1412.3884},
year = {2017}
}
Comments
23 pages. The original name of the paper is: Cluster algebras and minimal affinizations of representations of the quantum group of type $G_2$