  We review the Beilinson-Ginzburg construction of equivariant derived
categories of Harish-Chandra modules, and introduce analogues of Zuckerman
functors in this setting. They are given by an explicit formula, which works
equally well in the case of modules with a given infinitesimal character, which
is important if one wants to apply Beilinson-Bernstein localization. We also
show how to recover the usual Zuckerman functors from the equivariant ones by
passing to cohomology.
