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

Fu Hongchen; Ge Molin

近期发现有不法分子冒充我刊与作者联系，借此进行欺诈等不法行为，请广大作者加以鉴别，如遇诈骗行为，请第一时间与我刊编辑部联系确认（《中国物理C》（英文）编辑部电话：010-88235947,010-88236950），并作报警处理。

本刊再次郑重声明：

（1）本刊官方网址为cpc.ihep.ac.cn和https://iopscience.iop.org/journal/1674-1137

（2）本刊采编系统作者中心是投稿的唯一路径，该系统为ScholarOne远程稿件采编系统，仅在本刊投稿网网址（https://mc03.manuscriptcentral.com/cpc）设有登录入口。本刊不接受其他方式的投稿，如打印稿投稿、E-mail信箱投稿等，若以此种方式接收投稿均为假冒。

（3）所有投稿均需经过严格的同行评议、编辑加工后方可发表，本刊不存在所谓的“编辑部内部征稿”。如果有人以“编辑部内部人员”名义帮助作者发稿，并收取发表费用，均为假冒。

《中国物理C》（英文）编辑部

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

Abstract
HTML
Reference
Related

PDF

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.

[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]	Wei Lianfu , Wang Shunjin , Jie Quanlin . q-Analogue Boson Inverse Operators and Their Application. Chinese Physics C, 1997, 21(11): 1031-1034.
[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-Analog Boson Inverse Operators and Their Application. Chinese Physics C, 1997, 21(S4): 99-103.
[9]	Dai Qirun , Ma Zhanqing , Zhao Shusong , . Fermi-Dirac Correlation and Q^－v)K_v(Q) Distribution. Chinese Physics C, 1996, 20(11): 1014-1020.
[10]	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.
[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)_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.

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(514)
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

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.