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.

引用

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页码：1593 / 1627

页数：35

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