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

  • 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

  • 1 Department of Physics, Northeast Normal University, Changchu, Jilin, China;
  • 2 Theoretical Physics Division, Nankai Institute of Mathematics, Tianjin, China
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.

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