Crystal bases for the quantum queer superalgebra

被引：17
|
作者：
Grantcharov, Dimitar [1 ]
Jung, Ji Hye [2 ]
Kang, Seok-Jin [3 ,4 ]
Kashiwara, Masaki [5 ]
Kim, Myungho [6 ]
机构：
[1] Univ Texas Arlington, Dept Math, Arlington, TX 76021 USA
[2] Sogang Univ, Dept Math, Seoul 121742, South Korea
[3] Seoul Natl Univ, Dept Math Sci, Seoul 151747, South Korea
[4] Seoul Natl Univ, Res Inst Math, Seoul 151747, South Korea
[5] Kyoto Univ, Math Sci Res Inst, Kyoto 6068502, Japan
[6] Korea Inst Adv Study, Sch Math, Seoul 130722, South Korea
来源：
JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY | 2015年 / 17卷 / 07期
基金：
日本学术振兴会;
关键词：
Quantum queer superalgebras; crystal bases; odd Kashiwara operators; LITTLEWOOD-RICHARDSON RULE; Q-ANALOG; AFFINE ALGEBRAS; REPRESENTATIONS; COMBINATORICS;
D O I：
10.4171/JEMS/540
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We develop the crystal basis theory for the quantum queer superalgebra U-q(q(n)). We define the notion of crystal bases and prove the tensor product rule for U-q(q(n))-modules in the category Omicron(>= 0)(int) . Our main theorem shows that every U-q(q(n))-module in the category Omicron(>= 0)(int) has a unique crystal basis.
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页码：1593 / 1627
页数：35
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