  We construct an exact functor from the category of Harish-Chandra modules of
$\mathrm{GL}_n(\mathbb C)$ to the category of finite-dimensional modules of
graded Hecke algebras of type A. We show that the functor preserves
parabolically induced modules, standard modules, irreducible modules, unitary
modules and Dirac series. We also use the functor to connect a
Bernstein-Zelevinsky type functor for graded Hecke algebra side to the tensor
product for $\mathrm{GL}_n(\mathbb C)$ side. Some applications are also
discussed.
