Journal of Lie Theory

no. 4
Three-Term Recurrence Relations of Minimal Affinizations of Type G2
Journal of Lie Theory, Volume 27 (2017) no. 4, pp. 1119-1140
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.
DOI: 10.5802/jolt.986
Classification: 17B37
Keywords: Quantum affine algebras of type G-2, minimal affinizations, q-characters, Frenkel-Mukhin algorithm, M-systems, cluster algebras 
@article{JOLT_2017_27_4_a12,
     author = {J.-R. Li and L. Qiao},
     title = {Three-Term {Recurrence} {Relations} of {Minimal} {Affinizations} of {Type} {G\protect\textsubscript{2}}},
     journal = {Journal of Lie Theory},
     pages = {1119--1140},
     year = {2017},
     volume = {27},
     number = {4},
     doi = {10.5802/jolt.986},
     zbl = {1430.17048},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.986/}
}
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J.-R. Li; L. Qiao. Three-Term Recurrence Relations of Minimal Affinizations of Type G2. Journal of Lie Theory, Volume 27 (2017) no. 4, pp. 1119-1140. doi: 10.5802/jolt.986

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