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

YU Zu-Rong

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

Abstract
HTML
Reference
Related

PDF

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.

[1]	Jun-Long Tian , Hai-Tao Cui , Teng Gao , Ning Wang . Effect of Wigner energy on the symmetry energy coefficient in nuclei. Chinese Physics C, 2016, 40(9): 094101. doi: 10.1088/1674-1137/40/9/094101
[2]	MA Kai , WANG Jian-Hua , YUAN Yi . Wigner function for the Dirac oscillator in spinor space. Chinese Physics C, 2011, 35(1): 11-15. doi: 10.1088/1674-1137/35/1/003
[3]	HUANG Shi-Zhong , RUAN Tu-Nan , WU Ning , ZHENG Zhi-Peng . Bargmann-Wigner Equation and High Spin Field Equations. Chinese Physics C, 2001, 25(11): 1058-1064.
[4]	SHI Kang-Jie , FAN Heng , YUE Rui-Hong , ZHAO Shao-You , HOU Bo-Yu . Coefficient Algebra of the Minimal Representation of the Elliptic Quantum Group. Chinese Physics C, 2001, 25(7): 628-635.
[5]	Zhao Liu . Oscillator Algebra With Reflecting Boundary and Generalized Statistics. Chinese Physics C, 1997, 21(1): 25-33.
[6]	Xie Mi , Jin Baiqi , Ma Zhongqi . L^± Operators and Quantum Enveloping Algebras. Chinese Physics C, 1996, 20(7): 617-624.
[7]	Yu Zhaoxian , Yu Ge , Zhang Dexing , Liu Yehou . Nodvik and Holstein-Primakoff Realizations for Two-ParameterDeformed Quantum Algebra SU(1,1)_(q,s). Chinese Physics C, 1996, 20(12): 1082-1086.
[8]	Yu Zhaoxian , Liu Yehou , Li Qinglin , Liang Bifang . Study of SU(2)_q,s Coherent State by Using (q,s) Deformed Harmonic Oscillators of SU(2)_q,s Quantum Algebra. Chinese Physics C, 1995, 19(3): 258-263.
[9]	Zhou Huanqiang , He Jingsong , Guan Xiwen . Some Remarks on a Two-Parameter Quantum Algebra SU_qs(2) and a Two-Parameter Deformed Harmonic Oscillator. Chinese Physics C, 1995, 19(5): 420-423.
[10]	FU Hong-Chen , GE Mo-Lin . Cyclic Representations of Quantum (Super) Algebras At q^p=1. Chinese Physics C, 1993, 17(8): 700-709.
[11]	WU Ke , GUO Han-Ying , ZHANG Ren-Jie . Quantum Double and Quantum Double Pair——A Relation Between Quantum Algebras and Quantum Groups. Chinese Physics C, 1993, 17(3): 262-267.
[12]	YANG Ya-Ping , YU Zu-Rong . Irreducible Representation of Quantum Algebra SU_q(4). Chinese Physics C, 1993, 17(5): 423-430.
[13]	FU Hong-Chen , GE Mo-Lin . Verma Module of Quantum Group GL(3)_q Its q-Boson Realization and Cyclic Representations. Chinese Physics C, 1992, 16(10): 912-918.
[14]	YU Zu-Rong . Irreducible Representations of Quantum Lie Superalgebra SL_q(2/1). Chinese Physics C, 1992, 16(11): 1035-1042.
[15]	HU Zhan-Ning . Central Extension of the Quantum Deformed Virasoro Algebra. Chinese Physics C, 1991, 15(10): 898-905.
[16]	CHEN Ren . STOCHASTIC QUANTIZATION WITH SPIN 3/2 FIELD. Chinese Physics C, 1987, 11(2): 157-163.
[17]	FAN Hong-Yi , RUAN Tu-Nan . SOME APPLICATIONS OF COHERENT STATE FORMULATION OF THE WIGNER OPERATOR. Chinese Physics C, 1985, 9(1): 19-33.
[18]	FAN Hong-Yi , RUAN Tu-Nan . SU(3) CHARGED, HYPERCHARGED COHERENT STATE AND THE COLOR QUANTUM NUMBER. Chinese Physics C, 1984, 8(4): 416-425.
[19]	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.
[20]	ZENG GAO-JIAN . THE ACTION OF WIGNER OPERATOR OF SU₃ GROUP. Chinese Physics C, 1981, 5(2): 217-226.

Access

Get Citation

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

RIS(for EndNote,Reference Manager,ProCite)

BibTex

Txt

Milestone

Received: 1900-01-01
Revised: 1900-01-01

Article Metric

Article Views(2498)
PDF Downloads(416)
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

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).