Coefficient Algebra of the Minimal Representation of the Elliptic Quantum Group

SHI Kang-Jie; FAN Heng; YUE Rui-Hong; ZHAO Shao-You; HOU Bo-Yu

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2024年10月30日

Chinese Physics C> 2001, Vol. 25> Issue(7) : 628-635

Coefficient Algebra of the Minimal Representation of the Elliptic Quantum Group

Institute of Modern Physics, Northwest University, Xi'an 710069, China

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Abstract：
The algebra of the coefficients in the minimal representation of the An-1 quantum group, discussed by Felder and Varchenko, is given in this paper. Those coefficients are associated with the Boltzmann weights of A(1)n-1 interaction-round-a-face model. We show that the algebra satisfies the Yang-Baxter equation. The PBW base for this algebra is also given.

References

[1]

. Ruijsenaars S N M .Commun .Math .Phys.,1987,110 :191 2. Calogero F .Lett.Nuovo Cimento ,1975,13:4113. Moser J.Adv.Math.,1975,16 :4414. D'Hoker E ,Phong D H .Nucl.Phys.,1988,B513:4055. Gorsky A ,Krichever I,Marshakov A et al.Phys.Lett.,1995,B355:466 6. Jimbo M ,Miwa T ,Okado M .Lett.Math.Phys .,1987,14 :123 7. Jimbo M ,Miwa T ,Okado M .Commun.Math.Phys.,1988,116 :507 8. Jimbo M ,Miwa T ,Okado M ,Commun.Math.Phys.,1988,119:543— 5659. Gervais J L,Neveu A .Nucl.Phys.,1984 ,B2 38:12 5 10. Felder G ,Varchenko A .Commun.Math .Phys.,1996 ,181:74 111311. Kulish P P ,Reshetikhin N Y ,Sklyanin E K .Lett. Math .Phys.,1981,5:393 12. Sklyanin E K .Funct. Anal. Appl.,1982,16 :26313. Cherednik I V .Funct. Anal. Appl.,1985,19:7714. HOU B Y,WEI H .J.Math .Phys .,1989,30 :2750 15. Quano Y H ,Fujii A .Mod.Phys.Lett.,1991,A6:3635 16. Belavin A A .Nucl.Phys.,1981,B180:189 17. Richey M P ,Tracy C A .J Stat.Phys.,1986,42:311 18. Tracy C A.Physica ,1985,D16:203

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SHI Kang-Jie, FAN Heng, YUE Rui-Hong, ZHAO Shao-You and HOU Bo-Yu. Coefficient Algebra of the Minimal Representation of the Elliptic Quantum Group[J]. Chinese Physics C, 2001, 25(7): 628-635.

SHI Kang-Jie, FAN Heng, YUE Rui-Hong, ZHAO Shao-You and HOU Bo-Yu. Coefficient Algebra of the Minimal Representation of the Elliptic Quantum Group[J]. Chinese Physics C, 2001, 25(7): 628-635. shu

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Received: 2000-06-12
Revised: 1900-01-01

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1.
沈阳化工大学材料科学与工程学院沈阳 110142

Coefficient Algebra of the Minimal Representation of the Elliptic Quantum Group

Corresponding author: YUE Rui-Hong,

Institute of Modern Physics, Northwest University, Xi'an 710069, China

Received Date: 2000-06-12
Accepted Date: 1900-01-01
Available Online: 2001-07-05

Abstract: The algebra of the coefficients in the minimal representation of the An-1 quantum group, discussed by Felder and Varchenko, is given in this paper. Those coefficients are associated with the Boltzmann weights of A(1)n-1 interaction-round-a-face model. We show that the algebra satisfies the Yang-Baxter equation. The PBW base for this algebra is also given.