The Calogero-Sutherland model and polynomials with prescribed symmetry

The Schrodinger operators with exchange terms for certain Calogero-Sutherland quantum many-body systems have eigenfunctions which factor into the symmetric ground state and a multivariable polynomial. The polynomial tan be chosen to have a prescribed symmetry (i.e. be symmetric or antisymmetric) with respect to the interchange of some specified variables, For four particular Calogero-Sutherland systems we construct an eigenoperator for these polynomials which separates the eigenvalues and establishes orthogonality. In two of the cases this involves identifying new operators which commute with the corresponding Schrodinger operators, Tn each case we express a particular class of the polynomials with prescribed symmetry in a factored form involving the corresponding symmetric polynomials. (C) 1997 Published by Elsevier Science B.V.