利用Uq(sp(8))的向量表示实现辛型量子群O(Spq(8))

华东师范大学学报(自然科学版) ›› 2011, Vol. 2011 ›› Issue (3): 85-89.

利用U_q(sp(8))的向量表示实现辛型量子群O(Sp_q(8))

巩本学; 李莎莎

山东理工大学理学院, 山东淄博 255049

收稿日期:2010-04-01 修回日期:2010-07-01 出版日期:2011-05-25 发布日期:2011-05-25
通讯作者: 巩本学

Realization of quantum symplectic group O(Sp_q(8)) via vector representation of U_q(sp(8))

GONG Ben-xue; LI Sha-sha

College of Science, Shandong University of Technology, Zibo, Shandong 255049, China

Received:2010-04-01 Revised:2010-07-01 Online:2011-05-25 Published:2011-05-25
Contact: GONG Ben-xue

摘要/Abstract

摘要： Jantzen^[1]利用A型李代数A₂的量子包络代数U_q(sl₂(C)),借助于其表示论并利用R-矩阵的方法给出了SL_q(2)的定义关系式.本文对结构更为复杂的C型李代数做了类似的研究,通过U_q(sp(8))的表示理论实现了O(Sp_q(8))的定义关系式.

关键词: 辛型量子群, 实现, 向量表示, 辛型量子群, 实现, 向量表示

Abstract: To the quantum enveloping algebra U_q(sl₂(C)) of type A Lie algebra A₂, Jantzen gave the defining relations of SL_q(2) arising from the representations of U_q(sl₂(C)) by the R-matrix. This paper studied the similar question to U_q(sp(8)) of type C Lie algebra sp(8) which is more difficult than type A, and gave the realization of O(Sp_q(8)) arising from the representations of U_q(sp(8)) via Jantzen's approach.

Key words: realization, vector representation, quantum symplectic group, realization, vector representation

中图分类号:

O152.5

巩本学;李莎莎. 利用U_q(sp(8))的向量表示实现辛型量子群O(Sp_q(8))[J]. 华东师范大学学报(自然科学版), 2011, 2011(3): 85-89.

GONG Ben-xue;LI Sha-sha. Realization of quantum symplectic group O(Sp_q(8)) via vector representation of U_q(sp(8))[J]. Journal of East China Normal University(Natural Sc, 2011, 2011(3): 85-89.