2-D Cyclic Representations of Uq(sl(2)), C-G Coefficients,and a Free Fermion 8_Vertex Model

Zhang Jun; Yang Guangcan; Yan Hong

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《中国物理C》（英文）编辑部

2024年10月30日

Chinese Physics C> 1996, Vol. 20> Issue(S1) : 33-38

2-D Cyclic Representations of U_q(sl(2)), C-G Coefficients,and a Free Fermion 8_Vertex Model

Institute of Theoretical Physics, The Chinese Academy of Sciences, Beijing, China

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Abstract：
We construct explicitly the two-dimensional cyclic representation of quantum algebra U_q(sl(2)) with q=i and z central extension. The representation is irreducible and we write down explicitly the Clebsch-Gordan coefficients and the intertwiner of tensor representations in different orders. This intertwiner turns out to be an 8-vertex R-matrix that satisfies the free-Fermion condition and therefore gives an integrable model.
- quantum algebra ,
- cyclic representation ,
- intertwiner ,
- vertex model

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Zhang Jun, Yang Guangcan and Yan Hong. 2-D Cyclic Representations of U_q(sl(2)), C-G Coefficients,and a Free Fermion 8_Vertex Model[J]. Chinese Physics C, 1996, 20(S1): 33-38.

Zhang Jun, Yang Guangcan and Yan Hong. 2-D Cyclic Representations of U_q(sl(2)), C-G Coefficients,and a Free Fermion 8_Vertex Model[J]. Chinese Physics C, 1996, 20(S1): 33-38. shu

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Received: 1994-10-25

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Supported by the National Natural Science Foundation of China.

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沈阳化工大学材料科学与工程学院沈阳 110142

2-D Cyclic Representations of U_q(sl(2)), C-G Coefficients,and a Free Fermion 8_Vertex Model

Institute of Theoretical Physics, The Chinese Academy of Sciences, Beijing, China

Received Date: 1994-10-25

Fund Project: Supported by the National Natural Science Foundation of China.

Abstract: We construct explicitly the two-dimensional cyclic representation of quantum algebra U_q(sl(2)) with q=i and z central extension. The representation is irreducible and we write down explicitly the Clebsch-Gordan coefficients and the intertwiner of tensor representations in different orders. This intertwiner turns out to be an 8-vertex R-matrix that satisfies the free-Fermion condition and therefore gives an integrable model.