Jack polynomials and the multi-component Calogero-Sutherland model

Abstract

Using the ground state ψ0of a. multi-component generalization of the CalogeroSutherland 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 JK(1+1/λ), where λ is the coupling constant. The value of the normalization integral for ψ0Jk is conjectured, and some further related integrals are evaluated.