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

FU Hong-Chen; GE Mo-Lin

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2024年10月30日

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.

References

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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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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.

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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