Geodesic
Three-Term Recurrence Relations of Minimal Affinizations of Type G2
Journal of Lie theory, Tome 27 (2017) no. 4, pp. 1119-114
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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.
Classification : 17B37
Mots-clés : Quantum affine algebras of type G-2, minimal affinizations, q-characters, Frenkel-Mukhin algorithm, M-systems, cluster algebras 
@article{JLT_2017_27_4_JLT_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--114},
     year = {2017},
     volume = {27},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/JLT_2017_27_4_JLT_2017_27_4_a12/}
}
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J.-R. Li; L. Qiao. Three-Term Recurrence Relations of Minimal Affinizations of Type G2. Journal of Lie theory, Tome 27 (2017) no. 4, pp. 1119-114. http://geodesic.mathdoc.fr/item/JLT_2017_27_4_JLT_2017_27_4_a12/