A UNIFIED TREATMENT OF THE CHARACTERS OF SU(2) AND SU(1,1)

The character problems of SU(2) and SU(1,1) are re-examined from the s tandpoint of a physicist by employing the Hilbert space method which i s shown to yield a completely unified treatment for SU(2) and the disc rete series of representations of SU(1,1). For both the groups the pro blem is reduced to the evaluation of an integral which is invariant un der rotation for SU(2) and Lorentz transformation for SU(1,1). The int egrals are accordingly evaluated by applying a rotation to a unit posi tion vector in SU(2) and a Lorentz transformation to a unit SO(2,1) ve ctor which is time-like for the elliptic elements and space-like for t he hyperbolic elements in SU(1,1). The details of the procedure for th e principal series of representations of SU(1,1) differ substantially from those of the discrete series. (C) 1997 American Institute of Phys ics.