Cubic Dirac cohomology for generalized Enright-Varadarajan modules

For a complex semisimple Lie algebra g = h ⊕ v where h is a quadratic subalgebra and h and v are orthogonal with respect to the Killing form, we construct a large family of (g, h)-modules with non-zero cubic Dirac co-homology. Our method uses analogue of the construction of generalized Enright- Varadarajan modules for what we call (h, v) -split parabolic subalgebras. This family of modules includes discrete series representations and Aq(λ)-modules