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

Li Qiao; Jian-Rong Li

paper

Three-term recurrence relations of minimal affinizations of type $G_{2}$

arXiv:1412.3884

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.

arXiv comment23 pages. The original name of the paper is: Cluster algebras and minimal affinizations of representations of the quantum group of type $G_{2}$

Three-term recurrence relations of minimal affinizations of type G2​

Abstract

Three-term recurrence relations of minimal affinizations of type $G_{2}$