Two Dimensional Cyclic Representations of U<SUB>q</SUB>(sl<SUB>2</SUB>)and 8-Vertex Ising Model

Zhang Jun; Yang Guangcan; Yan Hong

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2024年10月30日

Chinese Physics C> 1995, Vol. 19> Issue(11) : 1005-1011

Two Dimensional Cyclic Representations of U_q(sl₂)and 8-Vertex Ising Model

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

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Abstract：
We give explicitly the 2-dimensional cyclic representations of quantum algebra U_q(sl₂)with central extension.The intertwiner for tensor representations in different ordersis constructed with C-G coefficients.This intertwiner is shown to be the R -matrix for eight vertex Ising model.

References

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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 quantum groups at root of 1,Colloque Dixmier,471-506,Prog.Math.92,Birkhauser（1990）.[3] H.An-Yang 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,Publ.of RIMS,Kyoto Univ,27（1991）639.[6] E.Date et al,Commun.Math.Phys,137（1991）133.[7] E.Date et al,Publ.of RIMS,Kyo to Univ,27（1991）437.[8] W.A.Schnizer,Roots of unity:Representations of quantumgroups,preprint of RIMS,Kyoto Univ,RIMS-916（1993）.[9] .Murakami,The free-fermion model in presence of field related to the quantum group Uqsl2 of affine type and the multi-variable Alexander polynomial of links,preprint of RIMS,Kyoto Umv,RIMS-822（1991）.[10] C.Fan,F.Y.Wu,Phys.Rev,B2（1970）723.

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Zhang Jun, Yang Guangcan and Yan Hong. Two Dimensional Cyclic Representations of U_q(sl₂)and 8-Vertex Ising Model[J]. Chinese Physics C, 1995, 19(11): 1005-1011.

Zhang Jun, Yang Guangcan and Yan Hong. Two Dimensional Cyclic Representations of U_q(sl₂)and 8-Vertex Ising Model[J]. Chinese Physics C, 1995, 19(11): 1005-1011. shu

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Received: 1900-01-01
Revised: 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

Two Dimensional Cyclic Representations of U_q(sl₂)and 8-Vertex Ising 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: 1995-11-15

Abstract: We give explicitly the 2-dimensional cyclic representations of quantum algebra U_q(sl₂)with central extension.The intertwiner for tensor representations in different ordersis constructed with C-G coefficients.This intertwiner is shown to be the R -matrix for eight vertex Ising model.