Dirac Induction for Unimodular Lie Groups

AbstractIn this paper, we give a geometric realization of discrete series representations for unimodular Lie groups on the spaces of harmonic spinors by using Connes–Moscovici'sL2-Index theorem. Our work is a continuation of Atiyah–Schmid's geometric realization of discrete series representations for semisimple Lie groups and Connes–Moscovici's realization of square-integrable representations for nilpotent Lie groups