Irreducible unitary representations of SUp,q II: The continuous series

A class of irreducible unitary representations belonging to the continuous series of SUp,q is explicitly determined in a space composed of the Kroneck er product of three spaces of square integrable functions. The continuous s eries corresponds to a Cartan subgroup whose vector part has maximal dimens ion. These representations are distinguished by a parameter r = 1, 2,...,p for p less than or equal to q in SUp,q. For r = 0, one obtains the represen tations in the discrete series as in [5], and all representations in the co ntinuous series, for r not equal 0, are obtained explicitly.