ON THE IRREDUCIBLE REPRESENTATIONS OF THE SIMPLE LIE GROUPS I——THE TENSOR BASIS FOR THE INFINITESIMAL GENERATORS OF THE CLASSICAL SIMPLE LIE GROUPS

Sun Hong-zhou; Han Qi-zhi

Chinese Physics C> 1980, Vol. 4> Issue(5) : 588-599

ON THE IRREDUCIBLE REPRESENTATIONS OF THE SIMPLE LIE GROUPS I——THE TENSOR BASIS FOR THE INFINITESIMAL GENERATORS OF THE CLASSICAL SIMPLE LIE GROUPS

Abstract
HTML
Reference
Related

PDF

Abstract：
In this paper, we analyse the commutation relations of the infinitesimal generatorsof all simple classical Lie groups and establish a new basis for these generators, calledthe tensor basis. In tensor basis, the infinitesimal, generators can be written as somescalar operators, some sets of angular momentum operators and some sets of irreducibletensor operators. The commutation relations, of these operators are very simple andhave many regularities. By means of the method that has been used in the earlier papers, "On the irre-ducible representations of the compact simple Lie groups of rank 2, I,II,III" and thetensor basis, all the irreducible representations of the classical simple Lie groups canbe calculated systematically.

References

[1]

陈金全等,物理学报,27(1978),32-203,238;高能物理与核物理,3(1979),17.[2] G. Racah, Group Theory and Spectroscopy, Ergeb. Eaakt. Naturwiss, 37(1965), 28.[3] R. E. Behrends et al., Rev. Mod. Phys., 34 (1962), 1.[4] A. Salam, The Formalism of Lei Groups,in Theoretical Physics, Vienna: International Atomie Energy Agency, 1963, p 173.[5] 孙洪洲,高能物理与核物理,4(1980), 73; 137; 271.[6] 宋行长等,科学通报,(1980),105.[7] 孙洪洲等,阶化李代数SU(5/1)的不可约表示和一种可能的巨统一模型,1980年广州粒子物理讨论会文集.

[1]	ZHAO Hai-Feng , WU Zi-Yu , Sebilleau Didier . Multiple Scattering Theory in a General Basis. Chinese Physics C, 2007, 31(5): 452-457.
[2]	LI Xi-Guo , Marcello Baldo , SONG Jian-Jun , LIU Fang . Diffusion Equations in Lie Group Manifold. Chinese Physics C, 2001, 25(1): 86-88.
[3]	Tai An , Sa Benhao . String Tension and Production of Strange Particles. Chinese Physics C, 1998, 22(4): 346-350.
[4]	Li Xiulin . Polarization Tensors of H→Zrr. Chinese Physics C, 1998, 22(9): 819-822.
[5]	Chen Xiangjun , Zhang Weining , Liu Yiming . Semi-Classical Transport Equation of Quarks. Chinese Physics C, 1997, 21(10): 905-910.
[6]	Pan Feng . Dimension Formula and an Irreducible Basis of Brauer Algebras. Chinese Physics C, 1995, 19(8): 734-738.
[7]	JIANG Xiang-Dong , ZHOU Xian-Jian . General Forms of the Polarization Tensors of Z→3γ and γγ→γγ. Chinese Physics C, 1993, 17(10): 898-906.
[8]	YANG Ya-Ping , YU Zu-Rong . Irreducible Representation of Quantum Algebra SU_q(4). Chinese Physics C, 1993, 17(5): 423-430.
[9]	YU Zu-Rong . Irreducible Representations of Quantum Lie Superalgebra SL_q(2/1). Chinese Physics C, 1992, 16(11): 1035-1042.
[10]	YANG Huan-Xiong . Hamiltonian Formalism of WZNW Field Under Chevalley Basis. Chinese Physics C, 1992, 16(8): 696-703.
[11]	WANG Jia-Jun , SUN Hong-Zhou . α-ROW PARTITION AND IT'S APPLICATION. Chinese Physics C, 1990, 14(9): 842-850.
[12]	PAN Ji-Zhi , JIANG Huan-Qing . "ONE, TWO, INFINITY" MODEL FOR PRECOMPOUND REACTION AND NUCLEAR SIZE EFFECT. Chinese Physics C, 1984, 8(1): 99-104.
[13]	YAO Nai-Guo , YU Zu-Rong . THE PHYSICAL BASES OF THE THREE PARTICLE SYSTEM. Chinese Physics C, 1984, 8(6): 720-731.
[14]	SHI YI-JIN . SYMMETRY BASIS AND PHYSICAL BASIS UNDER THE L·S AND jj REPRESENTATIONS FOR DI-HADRON SYSTEM. Chinese Physics C, 1983, 7(6): 743-755.
[15]	WANG KE-LIN . GENERATING FUNCTIONAL AND STRUCTURE OF VACUUM. Chinese Physics C, 1981, 5(3): 378-380.
[16]	HAN QI-ZHI , SONG XING-CHANG , LI GEN-DAO , SUN HONG-ZHOU . IRREDUCIBLE REPRESENTATIONS OF THE GRADED LIE ALGEBRA SU(m/n). Chinese Physics C, 1981, 5(5): 546-553.
[17]	ZENG GAO-JIAN . THE IRREDUCIBLE REPRESENTATIONS AND THEIR OCCUPATION NUMBER IN DIRECT MULTIPLICATION OF IRREDUCIBLE REPRESENTATIONS OF SU₃ GROUP. Chinese Physics C, 1981, 5(1): 82-91.
[18]	Sun Hong-zhou . ON THE IRREDUCIBLE REPRESENTATIONS OF THE COMPACT SIMPLE LIE GROUPS OF RANK 2(II). Chinese Physics C, 1980, 4(2): 137-159.
[19]	Sun Hong-zhou . ON THE IRREDUCIBLE REPRESENTATIONS OF THE COMPACT SIMPLE LIE GROUPS OF RANK 2(III). Chinese Physics C, 1980, 4(3): 271-285.
[20]	Sun Hung-zhou . ON THE IRREDUCIBLE REPRESENTATIONS OF THE COMPACT SIMPLE LIE GROUPS OF RANK 2(I). Chinese Physics C, 1980, 4(1): 73-92.

Access

Get Citation

Sun Hong-zhou and Han Qi-zhi. ON THE IRREDUCIBLE REPRESENTATIONS OF THE SIMPLE LIE GROUPS I——THE TENSOR BASIS FOR THE INFINITESIMAL GENERATORS OF THE CLASSICAL SIMPLE LIE GROUPS[J]. Chinese Physics C, 1980, 4(5): 588-599.

RIS(for EndNote,Reference Manager,ProCite)

BibTex

Txt

Milestone

Received: 1979-07-23
Revised: 1900-01-01

Article Metric

Article Views(2662)
PDF Downloads(252)
Cited by(0)

Policy on re-use

To reuse of subscription content published by CPC, the users need to request permission from CPC, unless the content was published under an Open Access license which automatically permits that type of reuse.

通讯作者: 陈斌, bchen63@163.com

1.
沈阳化工大学材料科学与工程学院沈阳 110142

ON THE IRREDUCIBLE REPRESENTATIONS OF THE SIMPLE LIE GROUPS I——THE TENSOR BASIS FOR THE INFINITESIMAL GENERATORS OF THE CLASSICAL SIMPLE LIE GROUPS

Sun Hong-zhou
Han Qi-zhi

Received Date: 1979-07-23
Accepted Date: 1900-01-01
Available Online: 1980-10-05

Abstract: In this paper, we analyse the commutation relations of the infinitesimal generatorsof all simple classical Lie groups and establish a new basis for these generators, calledthe tensor basis. In tensor basis, the infinitesimal, generators can be written as somescalar operators, some sets of angular momentum operators and some sets of irreducibletensor operators. The commutation relations, of these operators are very simple andhave many regularities. By means of the method that has been used in the earlier papers, "On the irre-ducible representations of the compact simple Lie groups of rank 2, I,II,III" and thetensor basis, all the irreducible representations of the classical simple Lie groups canbe calculated systematically.