Normalization of the wavwfunction for the Calogero-Sutherland model with internal degrees of freedom

The exact normalization of a multicomponent generalization of the ground state wavefunction 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 mulicomponent generalization in a special two-component case.

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