Quantum Groups, Braiding Matrices and Coset Models

  • H. Itoyama
Part of the NATO ASI Series book series (NSSB, volume 245)


We discuss a few results on quantum groups in the context of rational conformal field theory with underlying affine Lie algebras. A vertex-height correspondence — a well-known procedure in solvable lattice models — is introduced in the WZW theory. This leads to a new definition of chiral vertex operator in which the zero mode is given by the q-Clebsch Gordan coefficients. Braiding matrices of coset models are found to factorize into those of the WZW theories. We briefly discuss the construction of the generators of the universal enveloping algebra in Toda field theories.


Quantum Group Conformal Block Braid Group Primary Field Coset Model 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    V. G. Drinfeld, Soviet Math. Dokl. 32, 254 (1985)Google Scholar
  2. [2]
    M. Jimbo, Lett. Math. Phys. 10, 63 (1985)MathSciNetADSMATHCrossRefGoogle Scholar
  3. [3a]
    E. Sklyanin, Func. Anal. and Appl., 16(1982) 263;MathSciNetCrossRefGoogle Scholar
  4. [3b]
    P. Kulish, and N. Reshetikhin , J. Soviet Math. 23, (1983) 2435CrossRefGoogle Scholar
  5. [4]
    M. Jimbo, Commun. Math. Phys. 102, 537 (1986).MathSciNetADSMATHCrossRefGoogle Scholar
  6. [5]
    C. N. Yang, Phys. Rev. Lett 19, 1312 (1967).MathSciNetADSMATHCrossRefGoogle Scholar
  7. [6]
    R. J. Baxter, Ann. Phys. (N. Y.) 70, 193 (1972).MathSciNetADSMATHCrossRefGoogle Scholar
  8. [7a]
    A. Tsuchiya and Y. Kanie, Lett. Math. Phys. 13 (1987) 303MathSciNetADSMATHCrossRefGoogle Scholar
  9. [7b]
    A. Tsuchiya and Y. Kanie, Adv. Stud. Pure Math. 16 (1988) 297MathSciNetGoogle Scholar
  10. [8a]
    T. Kohno, Contemp. Math. 78 (1988) 339MathSciNetCrossRefGoogle Scholar
  11. [8b]
    T. Kohno, Ann. Inst. Fourier 37 (1987) 139; Nagoya preprint, November 1988MathSciNetMATHCrossRefGoogle Scholar
  12. [9]
    H. Itoyama and A. Sevrin, ITP-SB-89–33, to appear in Int. Journ. Mod. Phys. AGoogle Scholar
  13. [10]
    H. Itoyama, ITP-SB-88–82, to appear in Phys. Lett. AGoogle Scholar
  14. [11]
    H. Itoyama and P. Moxhay, ITP-SB-89–57Google Scholar
  15. [12]
    V.G. Knizhnik and A. B. Zamolodchikov, Nucl. Phys. B247 (1984) 83MathSciNetADSCrossRefGoogle Scholar
  16. [13]
    G. Moore and N. Seiberg, Phys. Lett. 212B (1988) 441MathSciNetADSGoogle Scholar
  17. [14]
    H. Wenzl, Invent. Math. 92 (1988) 349MathSciNetADSMATHCrossRefGoogle Scholar
  18. [15]
    M. Jimbo, T. Miwa, and M. Okado, Commun.Math. Phys. 116 (1988) 507MathSciNetADSMATHCrossRefGoogle Scholar
  19. [16]
    R. P. Kulish, N. Yu. Reshetikhin, E. K. Sklyanin Lett. Math. Phys. 5 (1981) 393MathSciNetADSMATHCrossRefGoogle Scholar
  20. [17]
    E. Verlinde, Nucl. Phys., B300 [FS22] (1988) 360MathSciNetADSCrossRefGoogle Scholar
  21. [18]
    L. Alvarez-Gaume, G. Gomez and G. Sierra, Phys. Lett. 220B (1989) 142; Cern TH 5267/88MathSciNetADSGoogle Scholar
  22. [19]
    See, for example, B. M. McCoy, J. H. Perk and T. T. Wu Phys. Rev. Lett. 46 (1981) 757.MathSciNetADSCrossRefGoogle Scholar
  23. [20a]
    H. Itoyama and H. B. Thacker, Nucl. Phys. B320[FS](1989)541MathSciNetADSCrossRefGoogle Scholar
  24. [20a]
    H. Itoyama and H. B. Thacker, Nucl. Phys.B (Proc. Suppl.) 5A (1988) 9.ADSGoogle Scholar
  25. [21]
    H. Itoyama and H. B. Thacker, Phys. Rev. Lett. 58, 1395 (1987).MathSciNetADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1990

Authors and Affiliations

  • H. Itoyama
    • 1
  1. 1.Institute for Theoretical PhysicsState University of New York at Stony BrookStony BrookUSA

Personalised recommendations