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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 withprescribed Dirac cohomology. They proved that all holomorphic discrete seriesrepresentations can be constructed via Dirac induction. All discrete seriesrepresentations of the group $SO_{e}(4,1)$ are nonholomorphic. In this paper weprove that they can also be constructed using algebraic Dirac induction.

Construction of discrete series representations of $SO_{e}(4, 1)$ via algebraic Dirac induction