Multiparticle SUSY quantum mechanics and the representations of permutation group
M. V. Ioffe, A. I. Neelov
Abstract
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 decompositions of the superhamiltonian into block-diagonal form with elementary matrix components are constructed. Matrices of coefficients of these minimal blocks are shown to coincide with matrices of irreducible representations of permutations 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.
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