Zuckerman functor

The Zuckerman functor, often denoted as \( Z \), is a construction in the realm of representation theory, particularly in the context of Lie algebras and their representations. It is named after the mathematician Greg Zuckerman, who introduced it in relation to the study of representations of semisimple Lie algebras. The Zuckerman functor is a method for producing certain types of representations from a given representation of a Lie algebra.