Bosonic realization of algebras in the Calogero model

We study an N-body Calogero model in the SN-symmetric subspace of the positive definite Fock space. We construct a new algebra of SN-symmetric operators represented on the symmetric Fock space, and find a natural orthogonal basis by mapping the algebra onto the Heisenberg algebra. Our main result is the bosonic realization of non-linear dynamical symmetry algebra describing the structure of degenerate levels of the Calogero model.