SU(1,1), its connections with SU(2), and the vector model

A relation between representation functions (RF’s) of positive discrete unitary irreducible representations (UIR’s) of SU(1,1) and the RF’s of the UIR’s of SU(2) is given. The classical vector model is worked out for the positive discrete UIR’s of SU(1,1). Classical domains, probability densities, and algorithms for numerical computations of SU(1,1) RF’s and Clebsch–Gordan coefficients are derived, in full analogy with the SU(2) case.