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Cyclic monodromy matrices forsl(n) trigonometricR-matrices

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Abstract

The algebra of monodromy matrices forsl(n) trigonometricR-matrix is studied. It is shown that a generic finite-dimensional polynomial irreducible representation of this algebra is equivalent to a tensor product ofL-operators. Cocommutativity of representations is discussed and intertwiners for factorizable representations are written through the Boltzmann weights of thesl(n) chiral Potts model.

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References

  1. Baxter, R.J.: Exactly solved models in statistical mechanics. London: Academic Press 1982

    Google Scholar 

  2. Bazhanov, V.V.: Commun. Math. Phys.113, 471–503 (1987)

    Article  Google Scholar 

  3. Bazhanov, V.V., Kashaev, R.M., Mangazeev, V.V., Stroganov, Yu.G.: Commun. Math. Phys.138, 393–408 (1991)

    Article  Google Scholar 

  4. Bazhanov, V.V., Stroganov, Yu.G.: J. Stat. Phys.59, 799–817 (1990)

    Article  Google Scholar 

  5. Belavin, A.A.: Nucl. Phys.B180 [FS2], 189–200 (1981)

    Article  Google Scholar 

  6. Cherednik, I.V.: Theor. Math. Phys.43, 117–119 (1980)

    Article  Google Scholar 

  7. Cherednik, I.V.: Duke Math. J.54, no. 2, 563–577 (1987)

    Article  Google Scholar 

  8. De Concini, C., Kac, V.G.: Colloque Dixmier 471–506 (1989); Progr. in Math.92 Boston: Birkhäuser 1990

  9. Date, E., Jimbo, M., Miki, K., Miwa, T.: Commun. Math. Phys.137, 133–147 (1991)

    Article  Google Scholar 

  10. Date, E., Jimbo, M., Miki, K., Miwa, T.: Pac. J. Math.154, no. 1, 37–65 (1992)

    Google Scholar 

  11. Drinfeld, V.G.: Dokl. AN SSSR283, 1060–1064 (1985); Sov. Math. Dokl.32, 254–258 (1985)

    Google Scholar 

  12. Drinfeld, V.G.: Dokl. AN SSSR296, 13–17 (1987); Sov. Math. Dokl.36, 212–216 (1988)

    Google Scholar 

  13. Faddeev, L.D.: Soviet Sci. Rev., Sect. C: Math. Phys. Rev.1, 107–155 (1980)

    Google Scholar 

  14. Jimbo, M.: Commun. Math. Phys.102, 537–548 (1986)

    Article  Google Scholar 

  15. Jimbo, M.: Lett. Math. Phys.11, 247–252 (1986)

    Article  Google Scholar 

  16. Kashaev, R.M., Mangazeev, V.V.:N n(n−1)/2-StateR-matrix related withU q(sl(n)) algebra atq 2N=1. Preprint IHEP 92-32 1992

  17. Kashaev, R.M., Mangazeev, V.V., Nakanishi, T.: Nucl. Phys.B362, 563–585 (1921)

    Article  Google Scholar 

  18. Kulish, P.P., Reshetikhin, N.Yu., Sklyanin, E.K.: Lett. Math. Phys.5, 393–401 (1981)

    Article  Google Scholar 

  19. Kulish, P.P., Sklyanin, E.K.: Zap. nauch. semin. LOMI95, 129–160 (1980); (J. Sov. Math.19, 1596–1620 (1982))

    Google Scholar 

  20. Kulish, P.P., Sklyanin, E.K.: Lect. Notes Phys.151, 61–119 (1984)

    Google Scholar 

  21. Perk, J.H.H., Shultz, C.L.: Phys. Lett.A84, 407–410 (1981)

    Article  Google Scholar 

  22. Reshetikhin, N.Yu., Semenov-Tian-Shansky, M.A.: Lett. Math. Phys.19, 133–142 (1990)

    Article  Google Scholar 

  23. Reshetikhin, N.Yu., Takhtajan, L.A., Faddeev, L.D.: Alg. Anal.1, no. 1, 178–206 (1989); (Len. Math. J.1, no. 1, 193–226 (1989))

    Google Scholar 

  24. Sklyanin, E.K.: Func. Anal. Appl.16, 27–34 (1982)

    Google Scholar 

  25. Sklyanin, E.K.: Func. Anal. Appl.17, 273–284 (1983)

    Article  Google Scholar 

  26. Sklyanin, E.K.: Functional Bethe Ansatz. In: Kuperschmidt, B.A. (ed.) Integrable and Superintegrable Systems. Singapore: World Scientific 1990

    Google Scholar 

  27. Tarasov, V.O.: Theor. Math. Phys.63, 175–196 (1985)

    Article  Google Scholar 

  28. Tarasov, V.O.: Int. J. Mod. Phys. A7, Suppl. 1B, 963–975 (1992); Tsuchia, A., Eguchi, T., Jimbo, M. (eds.) RIMS Research Project (1992) infinite Analysis. Proceedings. Singapore: World Scientific 1992

    Article  Google Scholar 

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  1. Physics Department, Leningrad University, 198904, Leningrad, Russia

    Vitaly Tarasov

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  1. Vitaly Tarasov
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Communicated by H. Araki

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Tarasov, V. Cyclic monodromy matrices forsl(n) trigonometricR-matrices. Commun.Math. Phys. 158, 459–483 (1993). https://doi.org/10.1007/BF02096799

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  • DOI: https://doi.org/10.1007/BF02096799

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