ON THE IRREDUCIBLE REPRESENTATIONS OF THE COMPACT SIMPLE LIE GROUPS OF RANK 2(I)

Sun Hung-zhou

Chinese Physics C> 1980, Vol. 4> Issue(1) : 73-92

ON THE IRREDUCIBLE REPRESENTATIONS OF THE COMPACT SIMPLE LIE GROUPS OF RANK 2(I)

Sun Hung-zhou

Peking University

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In this paper, we analyse the commutation relations of the infintesimal opera-tors of the group SU₃ and find that the eight infinitesimal operators of the groupSU₃ can be written as a scalar operator A, three angular momentum operators (L₁,L_o, L_-1,)and two sets of the irreducible tensor operators of rank 1/2, （T_{±1/2，V_±1/2}）By means of the commutation relations of these operators, all irreducible represen-tations of the group SU₃ can be easily obtained. In this pape, the matrices corresponding to these operators in the irreduciblerepresentation（λμ）, are given; therefore the irreducible representation and its re-presentation space R^λμ are completely defined. Besides, a method for calculatingthe scalar factors of the reduction coefficients and the symmetric relations of thosefactors are also given. As examples, the scalar factors of the reduction coefficientsof （λμ）×（10）, （λμ）×（01）, （λμ）×（20） and （λμ）×（11） are calculated. In the last part of this paper, we define the irreducible tensor operators ofthe group SU₃ and prove the corresponding Wigner-Eckart theory. The method used in the discussion of the group SU₃ be extended to allof the compact simple Lie groups of rank 2 and we shall discuss them in two suc-ceeding papers.

References

[1]

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[20]	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.

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Sun Hung-zhou. ON THE IRREDUCIBLE REPRESENTATIONS OF THE COMPACT SIMPLE LIE GROUPS OF RANK 2(I)[J]. Chinese Physics C, 1980, 4(1): 73-92.

Sun Hung-zhou. ON THE IRREDUCIBLE REPRESENTATIONS OF THE COMPACT SIMPLE LIE GROUPS OF RANK 2(I)[J]. Chinese Physics C, 1980, 4(1): 73-92. shu

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Received: 1978-12-08
Revised: 1900-01-01

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通讯作者: 陈斌, bchen63@163.com

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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 COMPACT SIMPLE LIE GROUPS OF RANK 2(I)

Peking University

Received Date: 1978-12-08

Accepted Date: 1900-01-01

Available Online: 1980-02-05

Abstract: In this paper, we analyse the commutation relations of the infintesimal opera-tors of the group SU₃ and find that the eight infinitesimal operators of the groupSU₃ can be written as a scalar operator A, three angular momentum operators (L₁,L_o, L_-1,)and two sets of the irreducible tensor operators of rank 1/2, （T_{±1/2，V_±1/2}）By means of the commutation relations of these operators, all irreducible represen-tations of the group SU₃ can be easily obtained. In this pape, the matrices corresponding to these operators in the irreduciblerepresentation（λμ）, are given; therefore the irreducible representation and its re-presentation space R^λμ are completely defined. Besides, a method for calculatingthe scalar factors of the reduction coefficients and the symmetric relations of thosefactors are also given. As examples, the scalar factors of the reduction coefficientsof （λμ）×（10）, （λμ）×（01）, （λμ）×（20） and （λμ）×（11） are calculated. In the last part of this paper, we define the irreducible tensor operators ofthe group SU₃ and prove the corresponding Wigner-Eckart theory. The method used in the discussion of the group SU₃ be extended to allof the compact simple Lie groups of rank 2 and we shall discuss them in two suc-ceeding papers.

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