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The character problems of SU(2) and SU(1,1) are reexamined from thestandpoint of a physicist by employing the Hilbert space method which is shownto yield a completely unified treatment for SU(2) and the discrete series ofrepresentations of SU(1,1). For both the groups the problem is reduced to theevaluation of an integral which is invariant under rotation for SU(2) andLorentz transformation for SU(1,1). The integrals are accordingly evaluated byapplying a rotation to a unit position vector in SU(2) and a Lorentztransformation to a unit SO(2,1) vector which is time-like for the ellipticelements and space-like for the hyperbolic elements in SU(1,1). The details ofthe procedure for the principal series of representations of SU(1,1) differsubstantially from those of the discrete series.Comment: 31 pages, RevTeX, typos corrected. To be published in Journal of  Mathematical Physic

A unified treatment of the characters of SU(2) and SU(1,1)