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

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《中国物理C》（英文）编辑部

2024年10月30日

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

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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.

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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.

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

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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.