Verma Module of Quantum Group GL(3)q,and the q-boson Realization and Cyclic Representations

Fu Hongchen; Ge Molin

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2024年10月30日

Chinese Physics C> 1992, Vol. 16> Issue(S4) : 431-437

Verma Module of Quantum Group GL(3)_q,and the q-boson Realization and Cyclic Representations

Fu Hongchen ¹ ,
Ge Molin ²

1 Department of Physics, Northeast Normal University, Changchu, Jilin, China;
2 Theoretical Physics Division, Nankai Institute of Mathematics, Tianjin, China

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Abstract：
The structure and Verma module of the matrix element algebra A(3)_q of the quantum group GL(3)_q are studied using a similar method for studying the structure and Verma module of semisimple Lie algebras. The q-boson realization of A(2)_q is constructed from its Verma representation and the cyclic representation of A(3)_q is obtained in terms of the q-boson realization.

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[7]	Xie Wenfang . Q-Effect of Structures of 3-Particle Systems. Chinese Physics C, 1997, 21(5): 465-469.
[8]	Wei Lianfu , Wang Shunjin , Jie Quanlin . q-Analogue Boson Inverse Operators and Their Application. Chinese Physics C, 1997, 21(11): 1031-1034.
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[11]	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.
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[13]	CHEN Yong-Qing . q-Oscillator Representations of the Quantum Superalgebra spl_q(2,1). Chinese Physics C, 1993, 17(7): 631-635.
[14]	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.
[15]	HU Zhan-Ning . The q-Deformed KdV Equation. Chinese Physics C, 1991, 15(8): 765-768.
[16]	CHENG Hong-Bo . Gauged Q-stars. Chinese Physics C, 1991, 15(11): 991-996.
[17]	FU Hong-Chen . INHOMOGENEOUS DIFFERENTIAL REALIZATION,BOSON-FERMION REALIZATION OF LIE SUPERALGEBRA B(0,1) AND ITS REPRESENTATIONS. Chinese Physics C, 1990, 14(2): 126-135.
[18]	Fu Hongchen . Inhomogeneous Differential Realization, Boson-Fermion Realization of Lie Superalgebra B(0,1) and its Representations. Chinese Physics C, 1990, 14(S1): 27-37.
[19]	SHEN Qi-Xing , WU Ji-Min , LU Jing-Xian , ZHAO Pei-Ying . THE QCD BEHAVIOURS OF THE XF₃ (X, Q²) UP TO THE LEADING LOG IN THE NEUTRINO DEEPINELASTIC PROCESSES. Chinese Physics C, 1983, 7(3): 309-315.
[20]	HUANG CHAO-SHANG , DAI YUAN-BEN . THE PROCESS e⁺+e^-→π+q+q IN QUANTUM CHROMODYNAMICS. Chinese Physics C, 1981, 5(4): 412-416.

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Fu Hongchen and Ge Molin. Verma Module of Quantum Group GL(3)_q,and the q-boson Realization and Cyclic Representations[J]. Chinese Physics C, 1992, 16(S4): 431-437.

Fu Hongchen and Ge Molin. Verma Module of Quantum Group GL(3)_q,and the q-boson Realization and Cyclic Representations[J]. Chinese Physics C, 1992, 16(S4): 431-437. shu

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Received: 1992-12-02

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Supported in part by the National Natural Science Foundation of China

one of the authors (Fu) supported by the Jilin Provincial Science and Technology Foundation of China.

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1.
沈阳化工大学材料科学与工程学院沈阳 110142

Verma Module of Quantum Group GL(3)_q,and the q-boson Realization and Cyclic Representations

Fu Hongchen ^1,
Ge Molin ^2,

1 Department of Physics, Northeast Normal University, Changchu, Jilin, China;
2 Theoretical Physics Division, Nankai Institute of Mathematics, Tianjin, China

Received Date: 1992-12-02

Fund Project: Supported in part by the National Natural Science Foundation of China one of the authors (Fu) supported by the Jilin Provincial Science and Technology Foundation of China.

Abstract: The structure and Verma module of the matrix element algebra A(3)_q of the quantum group GL(3)_q are studied using a similar method for studying the structure and Verma module of semisimple Lie algebras. The q-boson realization of A(2)_q is constructed from its Verma representation and the cyclic representation of A(3)_q is obtained in terms of the q-boson realization.