Paper detail

Jack polynomials and the multi-component Calogero-Sutherland model

Using the ground state $ψ_0$ 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 $J_κ^{(1+1/λ)}$, where $λ$ is the coupling constant. The value of the normalization integral for $ψ_0 J_κ^{(1+1/λ)}$ is conjectured, and some further related integrals are evaluated.