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Invariants of linear combinations of transpositions

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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.

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Inozemtsev, V.I. Invariants of linear combinations of transpositions. Lett Math Phys 36, 55–63 (1996). https://doi.org/10.1007/BF00403251

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Mathematics Subject Classifications (1991)

  • 33E05
  • 58F07
  • 82B10

Key words

  • invariants of motion
  • elliptic interaction
  • Calogero-Moser equation