ORTHOGONALITY OF THE HI-JACK POLYNOMIALS ASSOCIATED WITH THE CALOGEROMODEL

Orthogonality of the Hi-Jack polynomials, which were introduced as the simultaneous eigenfunctions of the first and second conserved operato rs of the Calogero model, is proved by showing that they are non-degen erate simultaneous eigenfunctions for all the commuting conserved oper ators of the Calogero model. The fact that our definition of the Hi-Ja ck polynomials uniquely specifies the Hi-Jack polynomials, which is as sured by the triangularity with respect to the dominance order among t he Young tableaux, plays an essential role in our proof.