Letters in Mathematical Physics

, Volume 36, Issue 1, pp 55–63 | Cite as

Invariants of linear combinations of transpositions

  • V. I. Inozemtsev


It is shown that for a one-parameter set H N of linear combinations of N(N−1)/2 elementary transpositions {P jk } (1≤j<k≤N) at arbitrary natural N≥3, one can construct a variety {I m } (3≤m≤N) of operators which commute with H N . Being applied to SU(n) spin representations of the permutation group, this proves the integrability of 1D periodic spin chains with elliptic short-range interaction.

Mathematics Subject Classifications (1991)

33E05 58F07 82B10 

Key words

invariants of motion elliptic interaction Calogero-Moser equation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Inozemtsev, V. I., J. Stat. Phys. 59, 1143 (1990).Google Scholar
  2. 2.
    Bethe, H., Z. Phys. 71, 205 (1931).Google Scholar
  3. 3.
    Haldane, F. D. M., Phys. Rev. Lett. 60, 635 (1988) Shastry, B. S., Phys. Rev. Lett. 60, 639 (1988).CrossRefGoogle Scholar
  4. 4.
    Faddeev, L. D., in Integrable Models of 1+1-Dimensional Quantum Field Theory, Elsevier, Amsterdam, 1984.Google Scholar
  5. 5.
    Bernard, D., Gaudin, M., Haldane, F. D. M., and Pasquier, V., J. Phys. A 26, 5219 (1993).CrossRefGoogle Scholar
  6. 6.
    Fowler, M. and Minahan, J., Phys. Rev. Lett. 70, 2325 (1993).CrossRefGoogle Scholar
  7. 7.
    Shastry, B. S. and Sutherland, B., Phys. Rev. Lett. 71, 5 (1993).CrossRefGoogle Scholar
  8. 8.
    Krichever, I. M., Funct. Anal. Appl. 14(4), 45 (1980).Google Scholar

Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • V. I. Inozemtsev
    • 1
  1. 1.Laboratory of Theoretical PhysicsJINRDubnaRussia

Personalised recommendations