Jacquet modules and Dirac cohomology

We show that Dirac cohomology of the Jacquet module of a Harish-Chandra module is a Harish-Chandra module for the corresponding Levi subgroup. We obtain an explicit formula of Dirac cohomology of the Jacquet module for most of the principal series, based on our determination of Dirac cohomology of irreducible generalized Verma modules with regular infinitesimal characters.