Exclusion statistics, anyons, and integrable models

A rather intimate interconnection is reviewed between the exclusion statistics (Haldane) model, the fractional statistics (anyon) model, and integrable models of the Calogero-Sutherland type: The spectra of anyons in the lowest Landau level (LLL) of a strong magnetic field, of the one-dimensional exclusion statistics model, and of the Calogero model are essentially all the same. The same connection is to hold for distinguishable particles of several species. The connection between multi species LLL anyons and exclusion statistics is established. The spectrum of a conjectured multi species generalization of the Calogero model is known but its Hamiltonian is not