Functional Analysis and Its Applications

, Volume 37, Issue 2, pp 81–85 | Cite as

Central Elements of the Elliptic Yang–Baxter Algebra at Roots of Unity

  • A. A. Belavin
  • M. Jimbo
Article

Abstract

We give central elements of the Yang--Baxter algebra for the R-matrix of the eight-vertex model for the case in which the crossing parameter is a rational multiple of one of the periods.

eight-vertex model R-matrix Yang--Baxter algebra center Baxter intertwining vector 

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References

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    R. J. Baxter, Exactly Solved Models in Statistical Mechanics, Academic Press, 1982.Google Scholar
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    V. Tarasov, “Cyclic monodromy matrices for the R-matrix of the six-vertex model and the chiral Potts model with fixed boundaryconditions,” Int. J. Mod. Phys. A, 7, Suppl. 1B, 963–975 (1992).Google Scholar
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    E. Date, M. Jimbo, A. Kuniba, T. Miwa, and M. Okado, “Exactly solvable SOS models II: Proof of the star-triangle relation and combinatorial identities,” Adv. Stud. Pure Math., 16, 17–122 (1988).Google Scholar

Copyright information

© Plenum Publishing Corporation 2003

Authors and Affiliations

  • A. A. Belavin
    • 1
  • M. Jimbo
    • 2
  1. 1.L. D. Landau Institute for Theoretical PhysicsRussian Academy of SciencesRussia
  2. 2.Graduate School of Mathematical SciencesUniversity of TokyoJapan

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