2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/151826Integrability, 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.14pages, LaTeX file using fleqn.sty, to appear in the proceedings of the Workshop on the Calogero-Moser-Sutherland models in the CRM Series in Mathematical Physics (Springer-Verlag)Statistical MechanicsHigh Energy Physics - TheoryQuantum AlgebraExactly Solvable and Integrable Systemstext