Starting with Schur Weyl duality for classical Lie groups I will discuss Arakawa Suzuki functors associated to category O and then similar functors applied to real Lie groups which link (g,K) modules with finite dimensional modules for graded affine Hecke algebras or the affine type B/C Brauer algebra. These functors satisfy particular properties; they map principal series to principal series, irreducible modules to irreducible modules and preserve unitarity. We will then restrict to the general linear group, introduce Dirac cohomology for both the general linear group and the graded affine Hecke algebra and discuss ongoing work towards creating a functor that exhibits a link between the Dirac operators of the respective categories.