DIRAC INDUCTION FOR UNIMODULAR LIE-GROUPS

In this paper, we give a geometric realization of discrete series repr esentations for unimodular Lie groups on the spaces of harmonic spinor s by using Connes-Moscovici's L(2)-Index theorem. Our work is a contin uation of Atiyah-Schmid's geometric realization of discrete series rep resentations for semisimple Lie groups and Connes-Moscovici's realizat ion of square-integrable representations for nilpotent Lie groups. (C) 1997 Academic Press.