Integrability of SU(N) spin chains with elliptic exchange

For some one-parameter set H-N of linear combinations of N(N - 1)/2 element ary transpositions {P-jk} (1 less than or equal to j < k <less than or equa l to> N) at arbitrary natural N greater than or equal to 3 one can construc t a variety (I-m) (3 less than or equal to m less than or equal to N) of op erators 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.