Homomorphisms between generalized Verma modules

Abstract

Let g be a finite-dimensional complex semisimple Lie algebra and p a parabolic subalgebra. The first result is a necessary and sufficient condition, in the spirit of the Bernstein-Gelfand-Gelfand theorem on Verma modules, for Lepowsky's standard map between two generalized Verma modules for g to be zero. The main result gives a complete description of all homomorphisms between the generalized Verma modules induced from one-dimensional p-modules, in the hermitian symmetric situation.