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

Verma Module of Quantum GroupGL(3)_q,and theq-boson Realization and Cyclic Representations

Fu Hongchen¹,
Ge Molin²

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

Abstract
HTML
Reference
Related

PDF

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

[1]	A. Plastino,M. C. Rocca. Tsallis' quantum q-fields. Chinese Physics C, 2018, 42(5): 053102.doi:10.1088/1674-1137/42/5/053102
[2]	HAN Lei,WANG Hai-Jun. New method of applying conformal group to quantum fields. Chinese Physics C, 2015, 39(9): 093102.doi:10.1088/1674-1137/39/9/093102
[3]	Ali N,Atashbar Tehrani. Jacobi polynomials and non-singlet structure function F₂(x,Q²) up to N³LO. Chinese Physics C, 2010, 34(9): 1479-1481.doi:10.1088/1674-1137/34/9/077
[4]	JIANG Jun-Qin. Antibunching Effect of the Excited k-Boson q-Coherent States. Chinese Physics C, 2004, 28(1): 22-25.
[5]	WANG Zhong-Qing. Antibunching Effect of k-Boson q-Coherent States. Chinese Physics C, 2002, 26(6): 576-581.
[6]	Xie Wenfang. Q-Effect of Structures of 3-Particle Systems. Chinese Physics C, 1997, 21(5): 465-469.
[7]	Wei Lianfu,Wang Shunjin,Jie Quanlin. q-Analogue Boson Inverse Operators and Their Application. Chinese Physics C, 1997, 21(11): 1031-1034.
[8]	Wei Lianfu,Wang Shunjin,Jie Quanlin.q-Analog Boson Inverse Operators and Their Application. Chinese Physics C, 1997, 21(S4): 99-103.
[9]	Zhang Jun,Yang Guangcan,Yan Hong. 2-D Cyclic Representations ofU_q(sl(2)), C-G Coefficients,and a Free Fermion 8_Vertex Model. Chinese Physics C, 1996, 20(S1): 33-38.
[10]	Yu Zhaoxian,Liu Yehou,Li Qinglin,Liang Bifang. Study of SU(2)_q,sCoherent State by Using (q,s) Deformed Harmonic Oscillators of SU(2)_q,sQuantum Algebra. Chinese Physics C, 1995, 19(3): 258-263.
[11]	Hao Sanru,Li Guanghua,Long Junyan. q-Deformed Charged Fermion Coherent States and SU(3)Charged, Hypercharged Fermion Coherent States. Chinese Physics C, 1994, 18(10): 919-927.
[12]	WANG Baolin,QUE Jianzhong,ZHANG Qingying. On the Higher Order Effects of A Consistent Q Framework in the sd Interacting Boson Model. Chinese Physics C, 1993, 17(11): 1048-1054.
[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)_qIts 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 SuperalgebraB(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 THEXF₃(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.

Access

Get Citation

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

RIS(for EndNote,Reference Manager,ProCite)

BibTex

Txt

Milestone

Received: 1992-12-02

Fund

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.

Article Metric

Article Views(1684)
PDF Downloads(4)
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