Three-Term Recurrence Relations of Minimal Affinizations of Type G2

被引：0
|
作者：
Li, Jian-Rong [1 ,2 ,3 ]
Qiao, Li [4 ]
机构：
[1] Lanzhou Univ, Sch Math & Stat, Lanzhou 730000, Gansu, Peoples R China
[2] Weizmann Inst Sci, Dept Math, IL-7610001 Rehovot, Israel
[3] Hebrew Univ Jerusalem, Einstein Inst Math, IL-9190401 Jerusalem, Israel
[4] Lanzhou Univ, Dept Math, Lanzhou 730000, Gansu, Peoples R China
来源：
JOURNAL OF LIE THEORY | 2017年 / 27卷 / 04期
基金：
欧洲研究理事会; 中国国家自然科学基金;
关键词：
Quantum affine algebras of type G(2); minimal affinizations; q-characters; Frenkel-Mukhin algorithm; M-systems; cluster algebras; CLUSTER ALGEBRAS; QUANTUM GROUPS; GRADED LIMITS; Q-CHARACTERS; REPRESENTATIONS;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Minimal affinizations introduced by Chari form a class of modules of quantum affine algebras. In this paper, we introduce a system of equations satisfied by the q-characters of minimal affinizations of type G(2) which we call the M-system of type G(2). The M-system of type G(2) contains all minimal affinizations of type G(2) and only contains minimal affinizations. The equations in the M-system of type G(2) are three-term recurrence relations. The M-system of type G(2) is much simpler than the extended T-system of type G(2) obtained by Mukhin and the second author. We also interpret the three-term recurrence relations in the M-system of type G(2) as exchange relations in a cluster algebra constructed by Hernandez and Leclerc.
引用
收藏
页码：1119 / 1140
页数：22
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