In this chapter we review the basic constructions involved in cohomological induction, most notably the Zuckerman and Bernstein functors. Our definitions are slightly different from the ones available in the literature. For example, we do not use Hecke algebras which are basic ingredients in the definitions in [KV]. Also, we use a direct description of derived functors, including the g-action; this approach has its roots in [B], [W] and [DV], and it was fully developed in the setting of equivariant derived categories by D. Miličić and the second author, [MP1], [MP2], [MP3], [Pan1], [Pan2]. In particular, this will provide for a very simple treatment of the duality results.
KeywordsModule Versus Projective Resolution Forgetful Functor Levi Subgroup Exact Functor
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