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

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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.

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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

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Received: 1992-12-02

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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.

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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.