Advertisement

Letters in Mathematical Physics

, Volume 29, Issue 3, pp 175–182 | Cite as

Many boson realizations of universal nonlinearW-algebras, modified KP hierarchies, and graded lie algebras

Article

Abstract

An infinite number of free field realizations of the universal nonlinearŴ (N) (Ŵ 1+∞ (N) ) algebras, which are identical to the KP Hamiltonian structures, are obtained in terms ofp plusq scalars of different signatures withpq =N. They are generalizations of the Miura transformation, and naturally give rise to the modified KP hierarchies via corresponding realizations of the latter. Their characteristic Liealgebraic origin is shown to be the graded SL(p, q).

Mathematics Subject Classifications (1991)

35Q53 81T40 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Drinfeld, V. and Sokolov, V.J. Soviet Math. 30, 1975 (1985).Google Scholar
  2. 2.
    Zamolodchikov, A. B.,Theoret. Math. Phys. 65, 1205 (1985).Google Scholar
  3. 3.
    Yu, F. and Wu, Y.-S.,Phys. Rev. Lett. 68, 2996 (1992).Google Scholar
  4. 4.
    Zamolodchikov, A. B. and Fateev, V. A.,Nuclear Phys. B. 280 [FS18] 644 (1987); Fateev, V. A. and Lykyanov, S. L.,Internat. J. Modern Phys. A 3, 507 (1988).Google Scholar
  5. 5.
    Kupershmidt, B. A. and Wilson, G.,Invent. Math. 62, 403 (1981).Google Scholar
  6. 6.
    Yu, F. and Wu, Y.-S.,Nuclear Phys. B 373, 713 (1992).Google Scholar
  7. 7.
    Bakas, I.,Phys. Lett. B 228, 57 (1989); Pope, C., Romans, L., and Shen, X.,Phys. Lett. B 236, 173 (1990).Google Scholar
  8. 8.
    Dickey, L. A.,Ann. New York Acad. Sci. 491, 131 (1987).Google Scholar
  9. 9.
    Sato, M.,RIMS Kokyuroku 439 30 (1981); Date, E., Jimbo, M., Kashiwara, M., and Miwa, T., in M. Jimbo and T. Miwa (eds),Proc. RIMS Sympos. Nonlinear Integrable Systems, World Scientific, Singapore, 1983; Segal, G. and Wilson, G.Publ. IHES 61, 1 (1985).Google Scholar
  10. 10.
    Bakas, I., and Kiritsis, E., Maryland/Berkeley/LBL preprint UCB-PTH-91/44, LBL-31213 or UMD-PP-92/37, Sept. 1991.Google Scholar
  11. 11.
    Yu, F. and Wu, Y.-S.,Phys. Lett. B 294, 177 (1992).Google Scholar
  12. 12.
    Yu, F. and Wu, Y.-S., Utah preprint UU-HEP-92/12; 92/13.Google Scholar
  13. 13.
    Figueroa-O'Farrill, J. M., Mas, J., and Ramos, E., Preprint BONN-HE-92/20; 92/α. Google Scholar
  14. 14.
    Kac, V. G.,Adv. Math. 26, 8 (1977).Google Scholar
  15. 15.
    Yu, F., Stony Brook/Utah preprint ITP-SB-92-55/UU-HEP-92/22.Google Scholar
  16. 16.
    Bais, F. A., Bouwknegt, P., Surridge, M., and Schoutens, K.,Nuclear Phys. B 304 348, 371 (1988).Google Scholar
  17. 17.
    Schoutens, K., Sevrin, A., and van Nieuwenhuizen, P.Nuclear Phys. B 364, 584 (1991);371, 315 (1992).Google Scholar
  18. 18.
    Ito, K.,Nuclear Phys. B 370, 123 (1992).Google Scholar

Copyright information

© Kluwer Academic Publishers 1993

Authors and Affiliations

  • Feng Yu
    • 1
    • 2
  1. 1.Institute for Theoretical PhysicsState University of New YorkStony BrookUSA
  2. 2.Department of PhysicsUniversity of UtahSalt Lake CityUSA

Personalised recommendations