Dynamical symmetry algebra of the Calogero model

We study the dynamical symmetry algebra of the N-body Calogero model describing the structure of degenerate levels and demonstrate that the algebra is intrinsically polynomial. We discuss some general properties of an algebra of SN-symmetric operators acting on the SN-symmetric subspace of the Fock space for any statistical parameter ν. In the bosonic case (ν=0) we find the algebra of generators for every N. For ν≠0, we explicitly reproduce the finite algebra for the 4-particle model, demonstrating some general features of our construction.