Skip to main content
SpringerLink
Log in

Quantum groups and WZNW models

  • Published:
Communications in Mathematical Physics Aims and scope Submit manuscript

Abstract

An explanation of the appearance of quantum groups in chiral WZNW models is given. Invariance of the theory under quantum group action is discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Tsuchiya, A., Kanie, Y.: In: Conformal field theory and solvable lattice models. Adv. Stud. Pure Math.16, 297 (1988); Lett. Math. Phys.13, 303 (1987)

  2. Kohno, T.: Quantized universal enveloping algebras and monodromy of braid groups. In: Braids Contemp. Math., 78. Nagoya preprint, 1988

  3. Fröhlich, J.: Statistics of fields, the Yang-Baxter equation and the theory of knots and links. Lectures at Cargese 1987, to appear in Nonperturbative Quantum Field Theory. New York: Plenum Press

  4. Rehren, K.-H., Schroer, B.: Einstein causality and artin braids. FU preprint 88-0439

  5. Drinfeld, V.G.: Quasi-Hopf algebras and Knizhnik-Zamolodchikov equations. Kiev preprint ITP-89-43E

  6. Drinfeld, V.G.: Proc. of Int. Cong. of Math., 1986, p. 798

  7. Jimbo, M.: Lett. Math. Phys.10, 63 (1985)

    Article  Google Scholar 

  8. Faddeev, L., Reshetikhin, N.Yu., Takhtajian, L.A.: Quantization of Lie groups and Lie algebras. LOMI preprint, E-14-87, Algebra i Analiz1, 37 (1989) (in Russian)

    Google Scholar 

  9. Moore, G., Seiberg, N.: Commun. Math. Phys.123, 77 (1989)

    Article  Google Scholar 

  10. Moore, G., Seiberg, N.: Lectures on RCFT. Preprint RU-89-32 YCTP-P13-89

  11. Witten, E.: Commun. Math. Phys.121, 351 (1989)

    Article  Google Scholar 

  12. Witten, E.: Gauge theories and integrable lattice models. IAS preprint IASSNS-HEP-89/11

  13. Alekseev, A., Shatashvili, S.: Mod. Phys. Lett. A16, 1551 (1988)

    Google Scholar 

  14. Alekseev, A., Faddeev, L., Shatshvili, S.: Quantization of the symplectic orbis of the compact Lie group by means of the functional integral. Preprint LOMI 1988. J. Geom. Phys. (in press)

  15. Alekseev, A., Shatashvili, S.: Nucl. Phys.B33, 719 (1989)

    Article  Google Scholar 

  16. Alekseev, A., Shatashvili, S.: From geometric quantization to conformal field theory. Commun. Math. Phys.128, 197–212 (1990)

    Google Scholar 

  17. Gerasimov, A., Marshakov, A., Morozov, A., Olshanetsky, M., Shatashvili, S.: Wess-Zumino model as a theory of free fields, I, II, III, IV. Preprints ITEP-64-89, ITEP-70-89, ITEP-72-89, ITEP-74-89

  18. Gervais, J.-L., Neveu, A.: Nucl. Phys.B238, 125 (1984);B224, 329 (1983)

    Article  Google Scholar 

  19. Babelon, O.: Phys. Lett.B215, 523 (1988)

    Article  Google Scholar 

  20. Faddeev, L., Takhtajan, L.: Liouville model on the lattice. Lecture Notes in Phys. Vol. 246, p. 166. Berlin, Heidelberg, New York: Springer 1986

    Google Scholar 

  21. Belavin, A.A.: KdV equation andW-algebras. Lecture given at Taniguchi Foundation Symposium. Integrable models in quantum field theory and statistical physics Kyoto, 1988

  22. Bershadsky, M., Ooguri, H.: HiddenSL(n) symmetry in conformal field theories. Commun. Math. Phys.126, 49–83 (1989)

    Google Scholar 

  23. Moore, G., Resketikhin, N.: A comment on quantum group symmetry in conformal field theory. Preprint IASSNS-HEP-89/18

  24. Witten, E.: Gauge theories, vertex models, and quantum group. IASSNS-HEP-89/32

  25. Wakimoto, M.: Commun. Math. Phys.104, 605 (1986)

    Article  Google Scholar 

  26. Feigin, B., Frenkel, E.: Usp. Mat. Nauk.43, 227 (1988)

    Google Scholar 

  27. Zamolodchikov, A.: Unpublished

  28. Dotsenko, V.: Unpublished

  29. Bernard, D., Felder, G.: Fock representations and BRST cohomology inSL(2) current algebra, ETH-TH/89-26

  30. Nemeschanky, D.: Feigin-Fuks repressentation ofSU(2) Kac-Moody algebra/USC-89/012 Gawedzki, K.: Quadrature of conformal field theories. IHES preprint 1989

  31. Distler, J., Qiu, Z.: BRS cohomology and a Feigin-Fuks representation... CLNS-89/911

  32. Block, B.: Classical exchange algebras in the Wess-Zumino-Witten model. Tel-Aviv preprint TAUP 1753-89

  33. Semenov-Tian-Shansky, M.: Publ. RIMS Kyoto University21, 1237 (1985)

    Google Scholar 

  34. Sklyanin, E.: J. Sov. Math.19, 1546 (1982)

    Article  Google Scholar 

  35. Kirillov, A., Reshetikhin, N.: LOMI preprint E-9-88

  36. Felder, G., Fröhlich, J., Keller, G.: Braid matrices and structure constants for minimal models, Zürich preprint, 1989

  37. Knizhnik, V., Zamolodchikov, A.: Nucl. Phys.B247, 83 (1989)

    Article  Google Scholar 

  38. Faddeev, L.: Quantum groups, Leningrad preprint, 1989

  39. Cremmer, E., Gervais, J.-L.: The quantum group structure associated with non-linearly extended Virasoro algebra, LPTENS-89/19

  40. J.-L. Gervais: The quantum group structure of 2D gravity and minimal models, LPTENS-89/14

  41. Faddeev, L.: On the exchange matrix for WZNW model.132, 131–138 (1990)

    Google Scholar 

  42. Alekseev, A.: To be published

Download references

Author information

Author notes

  1. S. Shatashvili (Visitor)

    Present address: Enrico Fermi Institute, 5640 S. Ellis Ave, 60637, Chicago, IL

Authors and Affiliations

  1. Leningrad Steklov Mathematical Institute, Fontanka 27, SU-191011, Leningrad, USSR

    A. Alekseev & S. Shatashvili (Visitor)

Authors
  1. A. Alekseev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. Shatashvili
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by N. Yu. Reshetikhin

Supported by NSF-PHY-86-57788

Rights and permissions

Reprints and permissions

About this article

Cite this article

Alekseev, A., Shatashvili, S. Quantum groups and WZNW models. Commun.Math. Phys. 133, 353–368 (1990). https://doi.org/10.1007/BF02097372

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02097372

Keywords

Search

Navigation