Geodesic
Three-Term Recurrence Relations of Minimal Affinizations of Type G2
Jian-Rong Li1, 2, 3 ; Li Qiao4
1School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, P. R. China
2Dept. of Mathematics, Weizmann Institute of Science, Rehovot 7610001, Israel
3Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem 9190401, Israel
4Dept. of Mathematics, Lanzhou University, Lanzhou 730000, P. R. China
Journal of Lie Theory, Tome 27 (2017) no. 4, pp. 1119-1140

Voir la notice de l'article provenant de la source Heldermann Verlag

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

Jian-Rong Li  1 , 2 , 3   ; Li Qiao  4

1 School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, P. R. China
2 Dept. of Mathematics, Weizmann Institute of Science, Rehovot 7610001, Israel
3 Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem 9190401, Israel
4 Dept. of Mathematics, Lanzhou University, Lanzhou 730000, P. R. China 
Jian-Rong Li; Li Qiao. Three-Term Recurrence Relations of Minimal Affinizations of Type G2. Journal of Lie Theory, Tome 27 (2017) no. 4, pp. 1119-1140. http://geodesic.mathdoc.fr/item/JOLT_2017_27_4_a12/
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     author = {Jian-Rong Li and Li 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},
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     url = {http://geodesic.mathdoc.fr/item/JOLT_2017_27_4_a12/}
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