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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

Li Qiao
Dept. of Mathematics, Lanzhou University, Lanzhou 730000, P. R. China

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

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