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 S_N-symmetric operators acting on the S_N-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.