|
Journal of Lie Theory 27 (2017), No. 4, 1119--1140 Copyright Heldermann Verlag 2017 Three-Term Recurrence Relations of Minimal Affinizations of Type G2 Jian-Rong Li School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, P. R. China and: Dept. of Mathematics, Weizmann Institute of Science, Rehovot 7610001, Israel and: Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem 9190401, Israel lijr07@gmail.com Li Qiao Dept. of Mathematics, Lanzhou University, Lanzhou 730000, P. R. China qiaol12@lzu.edu.cn Minimal affinizations introduced by Chari form a class of modules of quantum affine algebras. We introduce in this paper a system of equations satisfied by the q-characters of minimal affinizations of type G2, which we call the M-system of type G2. The M-system of type G2 contains all minimal affinizations of type G2 and only contains minimal affinizations. The equations in the M-system of type G2 are three-term recurrence relations. The M-system of type G2 is much simpler than the extended T-system of type G2 obtained by Mukhin and the second author. We also interpret the three-term recurrence relations in the M-system of type G2 as exchange relations in a cluster algebra constructed by Hernandez and Leclerc. Keywords: Quantum affine algebras of type G-2, minimal affinizations, q-characters, Frenkel-Mukhin algorithm, M-systems, cluster algebras. MSC: 17B37 [ Fulltext-pdf (347 KB)] for subscribers only. |