Multiparticle SUSY quantum mechanics and representations of the permutation group

The method of multidimensional SUSY quantum mechanics is applied to the inv estigation of supersymmetrical N-particle systems on a line for the case of separable centre-of-mass motion. New decomposition of the super-Hamiltonia n into block-diagonal form with elementary matrix components is constructed . Matrices of coefficients of these minimal blocks are shown to coincide wi th matrices of irreducible representations of the permutation group SN, whi ch correspond to the Young tableaux (N - M, 1(M)). The connections with kno wn generalizations of N-particle Calogero and Sutherland models are establi shed.