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

下载

页码：1593 / 1627

页数：35

共 50 条

[41] Crystal bases for quantum generalized Kac-Moody algebras
Jeong, K
Kang, SJ
Kashiwara, M
PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 2005, 90 : 395 - 438
[42] Polyhedral realizations of crystal bases for modified quantum algebras of type A
Hoshino, A
Nakashima, T
COMMUNICATIONS IN ALGEBRA, 2005, 33 (07) : 2167 - 2191
[43] Crystal bases for quantum affine algebras and combinatorics of Young walls
Kang, SJ
PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 2003, 86 : 29 - 69
[44] Quantum queer superalgebras
Jung, Ji Hye
Kang, Seok-Jin
ALGEBRAIC GROUPS AND QUANTUM GROUPS, 2012, 565 : 81 - +
[45] On the Structure of Quantum Toroidal Superalgebra εm|n
Xiang Hua WU
Hong Da LIN
Hong Lian ZHANG
Acta Mathematica Sinica,English Series, 2023, (11) : 2117 - 2138
[46] On the Structure of Quantum Toroidal Superalgebra εm|n
Wu, Xiang Hua
Lin, Hong Da
Zhang, Hong Lian
ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2023, 39 (11) : 2117 - 2138
[47] QUANTUM SUPERALGEBRA UQOSP(2,2)
DEGUCHI, T
FUJII, A
ITO, K
PHYSICS LETTERS B, 1990, 238 (2-4) : 242 - 246
[48] Character and Dimension Formulae for Queer Lie Superalgebra (vol 333, pg 1465, 2015)
Su, Yucai
Zhang, R. B.
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2016, 342 (02) : 769 - 770
[49] An Elliptic Solution of the Classical Yang-Baxter Equation Associated with the Queer Lie Superalgebra
Nazarov, Maxim
ANNALES HENRI POINCARE, 2024, : 5339 - 5347
[50] COMBINATORIAL BASES FOR COVARIANT REPRESENTATIONS OF THE LIE SUPERALGEBRA gl(m|n)
Molev, A. I.
BULLETIN OF THE INSTITUTE OF MATHEMATICS ACADEMIA SINICA NEW SERIES, 2011, 6 (04): : 415 - 462

← 1 2 3 4 5 →