The character of the exceptional series of representations of SU(1,1)

The character of the exceptional series of representations of SU(1,1) is de termined by using Bargmann's realization of the representation in the Hilbe rt space H-sigma of functions defined on the unit circle. The construction of the integral kernel of the group ring turns out to be especially involve d because of the nonlocal metric appearing in the scalar product with respe ct to which the representations are unitary. Since the nonlocal metric disa ppears in the "momentum space," i.e., in the space of the Fourier coefficie nts the integral kernel is constructed in the momentum space, which is tran sformed back to yield the integral kernel of the group ring in H-sigma. The rest of the procedure is parallel to that for the principal series treated in a previous paper. The main advantage of this method is that the entire analysis can be carried out within the canonical framework of Bargmann. (C) 2000 American Institute of Physics. [S0022-2488(99)02312-9].