Dynamical symmetry algebra of the Calogero model

Abstract

We study the dynamical symmetry algebra of the N-body Calogero model describing the structure of degenerate levels and demonstrate that the algebra is intrisically 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 \nu. In the bosonic case (\nu=0) we find the algebra of generators for every N. For \nu\neq 0, we explicitly reproduce the finite algebra for the 4-particle model, demonstrating some general features of our construction.