Construction of discrete series representations of $S{O}_e(4,1)$ via algebraic Dirac induction

The notion of algebraic Dirac induction was introduced by P. Pand\v{z}i'{c} and D. Renard. This is a construction which gives representations with prescribed Dirac cohomology. They proved that all holomorphic discrete series representations can be constructed via Dirac induction. All discrete series representations of the group $S{O}_e(4,1)$ are nonholomorphic. In this paper we prove that they can also be constructed using algebraic Dirac induction.