Dirac Induction for Unimodular Lie Groups

In this paper, we give a geometric realization of discrete series representations for unimodular Lie groups on the spaces of harmonic spinors by using Connes–MoscoviciʹsL2-Index theorem. Our work is a continuation of Atiyah–Schmidʹs geometric realization of discrete series representations for semisimple Lie groups and Connes–Moscoviciʹs realization of square-integrable representations for nilpotent Lie groups.