RODRIGUES FORMULA FOR HI-JACK SYMMETRICAL POLYNOMIALS ASSOCIATED WITHTHE QUANTUM CALOGERO MODEL

The Hi-Jack symmetric polynomials, which are associated with the simul taneous eigenstates for the first and second conserved operators of th e quantum Calogero model, are studied. Using the algebraic properties of the Dunkl operators for the model, we derive the Rodrigues formula for the Hi-Jack symmetric polynomials. Some properties of the Hi-Jack polynomials and the relationships with the Jack symmetric polynomials and with the basis given by the QISM approach are presented. The Hi-Ja ck symmetric polynomials are strong candidates for the orthogonal basi s of the quantum Calogero model.