Advertisement

Communications in Mathematical Physics

, Volume 136, Issue 3, pp 607–623 | Cite as

CyclicL-operator related with a 3-stateR-matrix

  • V. V. Bazhanov
  • R. M. Kashaev
Article

Abstract

We consider the problem of constructing a cyclicL-operator associated with a 3-stateR-matrix related to theU q (sl(3)) algebra atq N =1. This problem is reduced to the construction of a cyclic (i.e. with no highest weight vector) representation of some twelve generating element algebra, which generalizes theU q (sl(3)) algebra. We found such representation acting inC N C N C N . The necessary conditions of the existence of the intertwining operator for two representations are also discussed.

Keywords

Neural Network Statistical Physic Complex System Nonlinear Dynamics High Weight 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bazhanov, V.V., Stroganov, Yu.G.: J. Stat. Phys.51, 799 (1990)Google Scholar
  2. 2.
    Au-Yang, H., McCoy, B.M., Perk, J.H.H., Tang, S., Yan, M.: Phys. Lett. A123, 219 (1987)Google Scholar
  3. 3.
    McCoy, B.M., Perk, J.H.H., Tang, S., Sah, C. H.: Phys. Lett. A125, 9 (1987)Google Scholar
  4. 4.
    Baxter, R.J., Perk, J.H.H., Au-Yang, H.: Phys. Lett. A128, 138 (1988)Google Scholar
  5. 5.
    Faddeev, L.D., Reshetikhin, N.Yu., Takhtajan, L.A.: Algebra i Analiz.1(1) 178 (1989)Google Scholar
  6. 6.
    Drinfeld, V.G.: Proc. ICM, p. 798. New York: Berkeley 1987Google Scholar
  7. 7.
    Jimbo, M.: Lett. Math. Phys.10, 63 (1985)Google Scholar
  8. 8.
    Baxter, R.J., Bazhanov, V.V., Perk, J.H.H.: Functional relations for transfer matrices of the Chiral potts model. Preprint CMA-R38-8, Canberra, 1989 [to appear in Int. J. Mod. Phys. (1990)]Google Scholar
  9. 9.
    Baxter, R.J.: Chiral potts model: Eigenvalues of the transfer matrix. Preprint ANU, Canberra, 1990Google Scholar
  10. 10.
    Bazhanov, V.V., Stroganov, Yu.G.: On integrable deformations of the Chiral Potts model. RIMS preprint, 1990 (to appear)Google Scholar
  11. 11.
    Fateev, V.A., Zamolodchikov, A.B.: Phys. Lett. A92, 37 (1982)Google Scholar
  12. 12.
    Kashiwara, M., Miwa, T.: Nucl. Phys. B257 [FS17], 121 (1986)Google Scholar
  13. 13.
    Albertini, G., McCoy, B.M., Perk, J.H.H.: Adv. Stud. Pure Math.19, 1 (1989)Google Scholar
  14. 14.
    Hasegava, K., Yamada, Y.: Algebraic derivation of brokenZ N-model. Phys. Lett. A (to appear 1990)Google Scholar
  15. 15.
    Cherrednik, I.V.: Teor. Mat. Fiz.43(1), 117–119 (1980)Google Scholar
  16. 16.
    Kulish, P.P., Sklyanin, E.K.: Zapiski nauch. semin LOMI vol.95, pp. 129–160Google Scholar
  17. 17.
    Babelon, O.: Nucl. Phys. B230, 241–249 (1984); Lubashenko, V.V.: Ph. D. Thesis, Kiev 1986Google Scholar
  18. 18.
    Date, E., Jimbo, M., Miki, K., Miwa, T.:R-matrix for cyclic representations of\(U_q (\widehat{sl}(3,C))\) atq 3=1. RIMS preprint, 1990Google Scholar
  19. 19.
    Fairlie, D.B.: Quantum deformations ofsu(2). Preprint IASSNS-HEP-89/61Google Scholar
  20. 20.
    Perk, J.H.H., Schultz, C.L.: Phys. Lett A84, 407 (1981)Google Scholar

Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • V. V. Bazhanov
    • 1
  • R. M. Kashaev
    • 1
  1. 1.Institute for High Energy PhysicsProtvinoUSSR

Personalised recommendations