Jack polynomials and the multi-component Calogero-Sutherland model

Abstract

Using the ground state $\psi_0$ of a multicomponent generalization of the Calogero-Sutherland model as a weight function, orthogonal polynomials in the coordinates of one of the species are constructed. Using evidence from exact analytic and numerical calculations, it is conjectured that these polynomials are the Jack polynomials $J_\kappa^{(1+1/\lambda)}$, where $\lambda$ is the coupling constant. The value of the normalization integral for $\psi_0 J_\kappa^{(1+1/\lambda)}$ is conjectured, and some further related integrals are evaluated.