Letters in Mathematical Physics

, Volume 21, Issue 2, pp 123–131 | Cite as

Quantum Berezinian and the classical capelli identity

  • M. L. Nazarov
Article

Abstract

We study a superanalogue of the Yangian of the Lie algebra glmℂ. We apply our constructions to invariant theory.

AMS subject classifications (1980)

15A72 81C40 

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References

  1. 1.
    Kirillov, A. N. and Reshetikhin, N. Yu., Lett. Math. Phys. 12, 199 (1986).Google Scholar
  2. 2.
    Kulish, P. P. and Sklyanin, E. K., in Integrable Quantum Field Theories (Lecture Notes in Phys. 151), Springer, Berlin, 1982, p. 61.Google Scholar
  3. 3.
    Manin, Yu. I., Comm. Math. Phys. 123, 163 (1989).Google Scholar
  4. 4.
    Drinfeld, V. G., Algebra and Analysis 1(2), 30 (1989) (in Russian).Google Scholar
  5. 5.
    Howe, R., Trans. Amer. Math. Soc. 313, 539 (1989).Google Scholar
  6. 6.
    Cherednik, I. V., Duke Math. J. 54, 563 (1987).Google Scholar
  7. 7.
    Berezin, F. A., Introduction to Algebra and Analysis with Anticommuting Variables, Moscow University Press, Moscow, 1982 (in Russian).Google Scholar
  8. 8.
    Scheunert, M., J. Math. Phys. 24, 2681 (1983).CrossRefGoogle Scholar
  9. 9.
    Sergeev, A. N., C.R. Acad. Sci. Bulg. 35, 573 (1982).Google Scholar
  10. 10.
    Berele, A., Trans. Amer. Math. Soc. 309, 581 (1988).Google Scholar
  11. 11.
    Olshanskii, G. I. and Prati, M. C., Nuovo Cimento 85A, 1 (1985).Google Scholar
  12. 12.
    Sklyanin, E. K., J. Phys. 21A, 2375 (1988).Google Scholar

Copyright information

© Kluwer Academic Publishers 1991

Authors and Affiliations

  • M. L. Nazarov
    • 1
  1. 1.Department of Mathematics, T.F.F.A.Moscow State UniversityMoscowU.S.S.R.

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