Multiparticle Susy Quantum Mechanics and the Representations of Permutation Group

The method of multidimensional SUSY Quantum Mechanics is applied to the investigation of supersymmetrical N−particle systems on a line for the case of separable center-of-mass motion. New decomposition of the superhamiltonian into block-diagonal form with elementary matrix components is constructed. Matrices of coefficients of these minimal blocks are shown to coincide with matrices of irreducible representations of permutation group SN , which correspond to the Young tableaux (N −M, 1M ). The connections with known generalizations of N−particle Calogero and Sutherland models are established.