Is There Any Relation Between N Pairs of Deformed Q-Bosons and Uq [OSP(1/2N)]?

  • Tchavdar D. Palev
  • Nedjalka I. Stoilova

Abstract

This paper is dedicated to Prof. L. C. Biedenharn on the occasion of his 70th birthday. Contrary to most of the speakers I (T.D.P.) have known personally Prof. Biedenharn only for about 5 years, since the time we had organized the Group theoretical colloquium in Varna 1987. Scientifically, however, I know him for more than 25 years. Prof. Biedenharn and collaborators were the first who gave a systematic derivation of the results of Gel’fand and Zetlin1 for the transformations of the gl(n) modules.2 I have used a lot of their ideas when defining the concept of a Gel’ fand-Zetlin basis for the Lie superalgebras gl(n/1) and gl(n/m).3 That is not the only example. The present contribution is also based on results Prof. Biedenharn has recently obtained in quantum groups.4 We have in mind the concept of deformed Bose creation and annihilation operators.4,5,6

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References

  1. 1.
    I. M. Gel’fand and M. L. Zetlin, Dokl.Akad.Nauk SSSR 71: 825(1950).Google Scholar
  2. 2.
    G. E. Baird and L. C. Biedenharn, J.Math.Phys. 4: 1449 (1963).MathSciNetADSCrossRefGoogle Scholar
  3. 3.
    T. D. Palev, Funkt. Anal. Appl. 21: 245 (1987); 23: 141 (1989); J.Math.Phys. 33: 1433 (1989).MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    L. C. Biedenharn, J.Phys. A22: L873 (1989).MathSciNetADSGoogle Scholar
  5. 5.
    A. J. Macfarlane, J.Phys. A22: 4581 (1989).MathSciNetADSGoogle Scholar
  6. 6.
    C. P. Sun and H. C. Fu, J.Phys. A22: L983 (1989).MathSciNetADSGoogle Scholar
  7. 7.
    T. Hayashi, Comm.Math.Phys. 127: 129 (1990).MathSciNetADSCrossRefGoogle Scholar
  8. 8.
    A. Ch. Ganchev and T. D. Palev, J.Math.Phys. 21: 797 (1980).MathSciNetADSMATHCrossRefGoogle Scholar
  9. 9.
    E. Celeghini, T. D. Palev and M. Tarlini, Mod.Phys.Lett. B5:187 (1991).MathSciNetADSGoogle Scholar
  10. 10.
    V. G. Kac, Lect. Notes Math. 626: 597 (1978).CrossRefGoogle Scholar
  11. 11.
    H. S. Green, Phys.Rev. 90: 270 (1953).ADSMATHCrossRefGoogle Scholar
  12. 12.
    R. Floreanini, V. P. Spiridonov and L. Vinet, Comm.Math. Phys. 137: 149 (1991).MathSciNetADSMATHCrossRefGoogle Scholar
  13. 13.
    S. M. Khoroshkin and V. N. Tolstoy, Comm.Math.Phys. 141: 599 (1991).MathSciNetADSMATHCrossRefGoogle Scholar
  14. 14.
    T. D. Palev and V. N. Tolstoy, Comm.Math.Phys. 141: 549 (1991).MathSciNetADSMATHCrossRefGoogle Scholar
  15. 15.
    N. A. Ky, T. D. Palev and N. I. Stoilova, J.Math.Phys. 33: 1841 (1992).MathSciNetADSMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1993

Authors and Affiliations

  • Tchavdar D. Palev
    • 1
  • Nedjalka I. Stoilova
    • 1
  1. 1.Institute for Nuclear Research and Nuclear Energy BoulSofiaBulgaria

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