The CalogeroSutherland model and polynomials with prescribed symmetry
Abstract
The Schrödinger operators with exchange terms for certain CalogeroSutherland quantum manybody systems have eigenfunctions which factor into the symmetric ground state and a multivariable polynomial. The polynomial can 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 CalogeroSutherland 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 Schrödinger operators. In each case we express a particular class of the polynomials with prescribed symmetry in a factored form involving the corresponding symmetric polynomials.
 Publication:

Nuclear Physics B
 Pub Date:
 February 1997
 DOI:
 10.1016/S05503213(97)001120
 arXiv:
 arXiv:solvint/9609010
 Bibcode:
 1997NuPhB.492..682B
 Keywords:

 Nonlinear Sciences  Exactly Solvable and Integrable Systems;
 Mathematics  Quantum Algebra
 EPrint:
 LaTeX 2.09, 31 pages