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

Fu Hongchen; Ge Molin

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]	Zbigniew Drogosz , Wojciech Florkowski , Nikodem Witkowski , Radoslaw Ryblewski . ³H and ³He nuclei production in a combined thermal and coalescence framework for heavy-ion collisions in the few-GeV energy regime. Chinese Physics C, 2026, 50(2): 1-9.
[2]	Manpreet Kaur , Sushil Kumar , Sukhjeet Singh , A. K. Jain . Signature splitting in three-quasineutron rotational band 3/2[521]_ν$\otimes $1/2[660]_ν$\otimes $1/2[660]_νof ¹⁵⁵Dy. Chinese Physics C, 2025, 49(10): 104103. doi: 10.1088/1674-1137/ade95e
[3]	Ulaş Özdem . Unveiling the electromagnetic structure and intrinsic dynamics of spin-3/2 hidden-charm pentaquarks: A comprehensive QCD analysis. Chinese Physics C, 2025, 49(10): 103106. doi: 10.1088/1674-1137/ade95a
[4]	. SU(3) flavor symmetry analysis of hyperon non-leptonic two body decays. Chinese Physics C, 2025, 49(12): 123101. doi: 10.1088/1674-1137/adf1f1
[5]	Erdem Sucu , İzzet Sakallı . Quantum tunneling and Aschenbach effect in nonlinear Einstein-Power-Yang-Mills AdS black holes. Chinese Physics C, 2025, 49(10): 105101. doi: 10.1088/1674-1137/add8fe
[6]	Yu-xin Cheng , De-hao Zhao , Yue-yang Shao , Li Gong , Tao Wang , Xiao-shen Kang . SU(3) analysis for B(E2) anomaly. Chinese Physics C, 2025, 49(10): 104105. doi: 10.1088/1674-1137/aded05
[7]	Hao-Qiao Li , Hai-Ning Yan , Jiayin Gu , Xiao-Ze Tan . Probing Z/W pole physics at high-energy muon colliders via vector-boson-fusion processes. Chinese Physics C, 2025, 49(10): 103102. doi: 10.1088/1674-1137/addfcd
[8]	ZHANG Cong , HE Yuan , ZHAO Hong-Wei , ZHANG Sheng-Hu . Multipacting simulation and analysis of a taper quarter wave cavity by using Analyst-PT3P. Chinese Physics C, 2012, 36(4): 362-366. doi: 10.1088/1674-1137/36/4/012
[9]	Medina Ablikim , HUANG Wei-Cheng , . New Realization of N=2 Supersymmetric QuantumMechanics and Shape Invariance. Chinese Physics C, 2002, 26(4): 338-345.
[10]	Chen Zhongqiu , Shao Changgui , Ma Weichuan . Calculation of Wilson Loop Functionals for Classical and Quantum Gravities. Chinese Physics C, 1998, 22(3): 217-224.
[11]	Yang Jianjun , Ma Boqiang , Li Guanglie . Non-perturbative Quark Propagator and the Study of the Non-trivial Q² Dependence in the Nucleon Structure Functions. Chinese Physics C, 1997, 21(2): 146-156.

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(1139)
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.