Symmetric and non-symmetric bases of quantum integrable particle systems with long-range interactions

We study in inn algebraic manner the symmetric basis of the Calogero model and tile non-symmetric basis of the corresponding Calogero model with disti nguishable particles. The Rodrigues formulas are presented for the polynomi al parts of both bases. The square norm of the non-symmetric basis is evalu ated. Symmetrization of the non-symmetric basis reproduces the symmetric ba sis and enables us to calculate its square norm.