Informal Friday Seminar: Ciappara -- Tensor products of finite and infinite dimensional representations of semisimple Lie algebras

We begin a two-part study of Bernstein’s classic paper, "Tensor products of finite and
infinite dimensional representations of semisimple Lie algebras." In the first week, we
define projective functors (in relation to a fixed semisimple Lie algebra \frak{g}) and
derive some of their basic properties.  These properties are then applied in two
directions: first, to find equivalences between interesting categories of modules for
\frak{g}; and secondly, to find a correspondence between two-sided ideals of U(\frak{g})
and submodules of Verma modules, with Duflo’s Theorem as a corollary.