  Integrability, algebraic structures and orthogonal basis of the Calogero
model are studied by the quantum Lax and Dunkl operator formulations. The
commutator algebra among operators including conserved operators and
creation-annihilation operators has the structure of the W-algebra. Through an
algebraic construction of the simultaneous eigenfunctions of all the commuting
conserved operators, we show that the Hi-Jack (hidden-Jack) polynomials, which
are an multi-variable generalization of the Hermite polynomials, form the
orthogonal basis.
