Verma Module of Quantum Group GL(3)<SUB>q</SUB> Its q-Boson Realization and Cyclic Representations

FU Hong-Chen; GE Mo-Lin

Chinese Physics C> 1992, Vol. 16> Issue(10) : 912-918

Verma Module of Quantum Group GL(3)_q Its q-Boson Realization and Cyclic Representations

FU Hong-Chen ^, ,
GE Mo-Lin

Theoretical Physics Division,Nankai Institute of Mathematics Tianjin 300071

Abstract
HTML
Reference
Related

PDF

Abstract：
The structure and Verma module of matrix element algebra A(3)_q of 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(3)_q is constructed from its verma representation and the cyclic representation of A(3)_q is obtained in terms of the q-boson realization.

References

[1]

S. L. Woronowicz, Common. Math. Phys., 111(1987), 613; Publ. RIMS, 23(1987), 117;Yu. I. Manin, Quantum groups and noro-commutativer geometry, Centre des Recherches Mathematiciques,Montreal University report.[2] V. Drinfeld, Proc. ICM (Betkely, 1986) 793;M. Jimbo. Leo. Math. Phys.,. 10(1985), 63; 11 (1986), 247.[3] V. Drinfeld, Sov. Math, Dokl., 32(1985), 254;M. Jimbo, Common. Mash. Phys，102(1987), 537[4] L. A. Takhtajan, Lectures on quantum groups, in Introduction To Quantum Groups And Integrable Masrive Models of Quonrum Field Theosy (ed. by M. L. Ge and B. H. Zhao), World Scientific (1990).[5] E. G. Floratos, Phys. Lett., B233(1990), 395.[6] J. Weyers, Phys. Lett., B240(1990), 396.[7] R. Chakrabarti and R. Jagannathan, J. Phys., A24(1991), 1709[8] M. L. Ge, C. P. Sun and X. F. Liu, Phys. Lett., 1160(1991), 433.[9] H. C. Fu and M. L. Ge, The q-boson sealization of pasametsized cyclic sepsesentations of quantum algeb,as at qp=1, J. Math. Phys. 33(1992), 427.

[1]	Víctor Miguel Banda Guzmán , Rubén Flores-Mendieta , Johann Hernández . Use of SU(3) flavor projection operators to construct baryon-meson scattering amplitudes in the 1/N_c expansion. Chinese Physics C, 2026, 50(2): 1-25.
[2]	. 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(1): 014104. doi: 10.1088/1674-1137/ae099a
[3]	. Correlation between Zero-Sound modes and nuclear equation of state stiffness detected by light vector boson. Chinese Physics C, 2026, 50(1): 014101. doi: 10.1088/1674-1137/adfa81
[4]	Ali Çiçi , Hüseyin Dağ . Resolving the W boson Mass in the Lepton Specific Two Higgs Doublet Model. Chinese Physics C, 2026, 50(3): 1-19.
[5]	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
[6]	Bo Lan , Qin-Ze Song , Jin-Huan Sheng , Yi Qiao , Ru-Min Wang . Study of χ_cJ (J = 0,1,2) decays to light meson pairs based on SU(3) flavor symmetry/breaking analysis. Chinese Physics C, 2025, 49(12): 123106. doi: 10.1088/1674-1137/adff00
[7]	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
[8]	. 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
[9]	Liuxin Zhao , Honglei Li , Zhi-Long Han , Fei Huang , Xinyi Yan . Extra charged gauge boson W′ in Alternative Left-Right Model at future muon collider. Chinese Physics C, 2025, 49(12): 123102. doi: 10.1088/1674-1137/adec51
[10]	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
[11]	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
[12]	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
[13]	Medina Ablikim , HUANG Wei-Cheng , . New Realization of N=2 Supersymmetric QuantumMechanics and Shape Invariance. Chinese Physics C, 2002, 26(4): 338-345.
[14]	Chen Zhongqiu , Shao Changgui , Ma Weichuan . Calculation of Wilson Loop Functionals for Classical and Quantum Gravities. Chinese Physics C, 1998, 22(3): 217-224.
[15]	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 Hong-Chen and GE Mo-Lin. Verma Module of Quantum Group GL(3)_q Its q-Boson Realization and Cyclic Representations[J]. Chinese Physics C, 1992, 16(10): 912-918.

FU Hong-Chen and GE Mo-Lin. Verma Module of Quantum Group GL(3)_q Its q-Boson Realization and Cyclic Representations[J]. Chinese Physics C, 1992, 16(10): 912-918. shu

RIS(for EndNote,Reference Manager,ProCite)

BibTex

Txt

Milestone

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

Article Metric

Article Views(4588)
PDF Downloads(414)
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 Its q-Boson Realization and Cyclic Representations

FU Hong-Chen ^,
GE Mo-Lin

Corresponding author: FU Hong-Chen,

Theoretical Physics Division,Nankai Institute of Mathematics Tianjin 300071

Received Date: 1900-01-01
Accepted Date: 1900-01-01
Available Online: 1992-10-05

Abstract: The structure and Verma module of matrix element algebra A(3)_q of 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(3)_q is constructed from its verma representation and the cyclic representation of A(3)_q is obtained in terms of the q-boson realization.

HTML

Reference (1)

Link: IOPScience; SCOAP³; arXiv; Chinese Physical Society

Journal information: Introduction; Editorial Board; Others; Subscribe

Contact us: QQ: 1307685413; Tel: +86-010-88235947; Fax: +86-010-88233126; E-mail: cpc@ihep.ac.cn

CPC Website
IOP Website
CPC WeChat

Supported by: Beijing Renhe Information Technology Co. Ltd E-mail: info@rhhz.net

DownLoad: Full-Size Img PowerPoint

Return

Verma Module of Quantum Group GL(3)_q Its q-Boson Realization and Cyclic Representations

Abstract：

References

Access

Article Metrics

Metrics

通讯作者: 陈斌, bchen63@163.com

Email This Article

Verma Module of Quantum Group GL(3)_q Its q-Boson Realization and Cyclic Representations

Corresponding author: FU Hong-Chen,

HTML

目录

Verma Module of Quantum Group GL(3)q Its q-Boson Realization and Cyclic Representations

Abstract：

References

Access

Article Metrics

Metrics

通讯作者: 陈斌, bchen63@163.com

Email This Article

Verma Module of Quantum Group GL(3)q Its q-Boson Realization and Cyclic Representations

Corresponding author: FU Hong-Chen,

HTML

目录

Verma Module of Quantum Group GL(3)_q Its q-Boson Realization and Cyclic Representations

Verma Module of Quantum Group GL(3)_q Its q-Boson Realization and Cyclic Representations