Journal of Soviet Mathematics

, Volume 41, Issue 2, pp 916–924

Combinatorics, Bethe Ansatz, and representations of the symmetric group

  • S. V. Kerov
  • A. N. Kirillov
  • N. Yu. Reshetikhin
Article

Abstract

Techniques developed in the realms of the quantum method of the inverse problem are used to analyze combinatorial problems (Young diagrams and rigged configurations).

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Literature cited

  1. 1.
    H. Bethe, “Zur Theorie der Metalle. I. Eigenwerte und Eigenfunktionen der linearen Atom Kette,” Z. Physik,71, 205–226 (1931).Google Scholar
  2. 2.
    L. A. Takhtadzhyan and L. D. Faddeev, “Spectrum and scattering of stimuli in one-dimensional Heisenberg magnetics,” in: Differential Geometry, Lie Groups, and Mechanics. IV, J. Sov. Math.,24, No. 2 (1984).Google Scholar
  3. 3.
    A. N. Kirillov, “Combinatorial identities and completeness of states of Heisenberg magnetics,” in: Questions of Quantum Field Theory and Statistical Physics. 4, J. Sov. Math.,30, No. 4 (1985).Google Scholar
  4. 4.
    A. N. Kirillov, “Completeness of states of generalized Heisenberg magnetics,” in: Automorphic Functions and Number Theory. II, J. Sov. Math.,36, No. 1 (1987).Google Scholar
  5. 5.
    I. MacDonald, Symmetric Functions and Hall Polynomials [Russian translation], Moscow (1985).Google Scholar
  6. 6.
    D. Knuth, The Art of Computer Programming [Russian translation], Vol. 3, Moscow (1978).Google Scholar
  7. 7.
    S. V. Kerov and A. M. Vershik, “The characters of the infinite symmetric group and probability properties of the Robinson-Schensted-Knuth algorithm,” SIAM J. Alg. Disc. Math.,7, No. 1, 116–124 (1986).Google Scholar
  8. 8.
    A. N. Kirillov and N. Yu. Reshetikhin, “The Yangians, Bethe Ansatz and combinatorics,” Preprint, 1986.Google Scholar
  9. 9.
    P. P. Kulish and N. Yu. Reshetikhin, “Diagonalization of GL(N) invariant transfer matrices and quantum N-wave system (Lee model),” J. Phys. A,16, 591–596.Google Scholar
  10. 10.
    A. N. Kirillov and N. Yu. Reshetikhin, “Bethe Ansatz and combinatorics of Young tableaux,” this issue, pp. 65–115.Google Scholar

Copyright information

© Plenum Publishing Corporation 1988

Authors and Affiliations

  • S. V. Kerov
  • A. N. Kirillov
  • N. Yu. Reshetikhin

There are no affiliations available

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