Normalization of the Wavefunction for the Calogero-Sutherland Model with Internal Degrees of Freedom

The exact normalization of a multicomponent generalization of the ground state wave-function of the Calogero-Sutherland model is conjectured. This result is obtained from a conjectured generalization of Selberg’s N-dimensional extension of the Euler beta integral, written as a trigonometric integral. A new proof of the Selberg integral is given, and the method is used to provide a proof of the multicomponent generalization in a special two-component case.