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

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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.

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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.

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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

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Received: 1900-01-01
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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.

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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