Irreducible Representations and Wigner Coefficients of Quantum Algebra SL<SUB>q</SUB>(3)

YU Zu-Rong

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《中国物理C》（英文）编辑部

2024年10月30日

Chinese Physics C> 1992, Vol. 16> Issue(9) : 832-839

Irreducible Representations and Wigner Coefficients of Quantum Algebra SL_q(3)

YU Zu-Rong ^,

Department of Physics,Tongji University,Shanghai 200092

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Abstract：
In this paper,the irreducible representations and Wigner coefficients of SL_q(3) have been obtained.The generators of SL_q(3) satisfying the serre relations are considered as 1/2 rank tensor——like of SL_q(2).Their reduced matrix elements can be calculated by a set of recurrent formula.The isoscalar factors (ISF) of SL_q(3) can also be derived by them.This means that the Racah Factorization Lemma is also exact for the quantum algebra SL_q(3).

References

[1]

Zurong Yu, J. Phys., A24 (1991), L399.[2] 孙洪洲，中国科学14(1965),840.[3] Zhang-si Ma, J. Math. Phys., 31(1989), 550.[4] M. Jimbo, Lett. Math. Phys., 10(1985), 63,Lett. Math. Phys., 11(1986), 247.[5] Bo-yu Hou, et al., Cornmun. Theor. Phys., 13(1990).181,341.[6] H. Ruegg, J. Math. Phys., 31(1990),. 1085.[7] M. Nomur, J. Math. Phys.,30(1989), 2397.[8] L.I. Kachurik A.V. Klimyk, J. Phys., A23(1990).[9] L.L. Biedenharn, Lett. Math. Phys., 20(1990), 271.[10] M. Nomura, J. Phys. Soci. Japan.,59(1990), 2345.

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YU Zu-Rong. Irreducible Representations and Wigner Coefficients of Quantum Algebra SL_q(3)[J]. Chinese Physics C, 1992, 16(9): 832-839.

YU Zu-Rong. Irreducible Representations and Wigner Coefficients of Quantum Algebra SL_q(3)[J]. Chinese Physics C, 1992, 16(9): 832-839. shu

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Received: 1900-01-01
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Irreducible Representations and Wigner Coefficients of Quantum Algebra SL_q(3)

YU Zu-Rong ^,

Corresponding author: YU Zu-Rong,

Department of Physics,Tongji University,Shanghai 200092

Received Date: 1900-01-01
Accepted Date: 1900-01-01
Available Online: 1992-09-05

Abstract: In this paper,the irreducible representations and Wigner coefficients of SL_q(3) have been obtained.The generators of SL_q(3) satisfying the serre relations are considered as 1/2 rank tensor——like of SL_q(2).Their reduced matrix elements can be calculated by a set of recurrent formula.The isoscalar factors (ISF) of SL_q(3) can also be derived by them.This means that the Racah Factorization Lemma is also exact for the quantum algebra SL_q(3).