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Chinese Physics C> 1995, Vol. 19> Issue(12) : 1084-1089 

2-Dimensional Cyclic Representations of Uq(sl(2)), C-GCoefficients and a Free Fermion 8-Vertex Model

  •  Institute of Theoretical Physics,The Chinese Academy of Sciences, Beijing 100080

  • We give explicitly the 2-dimensional cyclic representations of quantum algebra Uq(sl(2)) with central extension. The C-G rule and the C-G coefficients are calculated and the intertwiner for tensor representations in different orders is constructed with C-G coefficients. This intertwiner is shown to be the R-matrix for an eight vertex model that satisfies the free Fermion condition and therefore gives an integrable model.
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  • References

    [1] 马中骐，杨-巴克斯特方程和量子包络代数，科学出版社，1993.[2] C.De Concini,V.G.Kac,Representations of quanum groups at root of 1,Colloque Dixmier,471-506,Prog.Math.92,Birkhauser（1990）.[3] H.Anyang et al,Phys.Lett,A123（1987）219.[4] V.V.Bazhanov,Yu. G.Stroganov,J.Stat.Phys.,59（1990）199.[5] E.Date et al.,RIMS,27（1991）639.[6] E.Date et al,Commun.Math.Phys,137（1991）133.[7] E.Date et al,RIMS,27（1991）437.[8] W.A.Schnizer,RIMS（1993）916.[9] C.Fan,F.Y.Wu,Phys.REV,B2（1970）723.[10] B.U.Felderhof,Physica,65（1973）421;Physica,66（1973）279.[11] J.Murakami,RIMS（1991）822.[12] M.Ruiz-Altaba,Phys.Lett,B279（1992）326.[13] R.Cuerno et al,IMAFF-2/93[14] R.Cuerno,A.Gonzalez-Ruir,IMAFF-11/93,LPTHE-PAR-21/93.[15] E.Lopez,IMAFF-12/93.

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Zhang Jun, Yang Guangcan and Yan Hong. 2-Dimensional Cyclic Representations of Uq(sl(2)), C-GCoefficients and a Free Fermion 8-Vertex Model[J]. Chinese Physics C, 1995, 19(12): 1084-1089.
Zhang Jun, Yang Guangcan and Yan Hong. 2-Dimensional Cyclic Representations of Uq(sl(2)), C-GCoefficients and a Free Fermion 8-Vertex Model[J]. Chinese Physics C, 1995, 19(12): 1084-1089. shu
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Received: 1900-01-01
Revised: 1900-01-01
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2-Dimensional Cyclic Representations of Uq(sl(2)), C-GCoefficients and a Free Fermion 8-Vertex Model

    Corresponding author: Zhang Jun,
  • Institute of Theoretical Physics,The Chinese Academy of Sciences, Beijing 100080
  • Received Date: 1900-01-01
  • Accepted Date: 1900-01-01
  • Available Online: 1995-12-05

Abstract: We give explicitly the 2-dimensional cyclic representations of quantum algebra Uq(sl(2)) with central extension. The C-G rule and the C-G coefficients are calculated and the intertwiner for tensor representations in different orders is constructed with C-G coefficients. This intertwiner is shown to be the R-matrix for an eight vertex model that satisfies the free Fermion condition and therefore gives an integrable model.

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