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Letters in Mathematical Physics

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

Invariants of linear combinations of transpositions

  • V. I. Inozemtsev
Article

Abstract

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 

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Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

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

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