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.