Projective functors and the restriction of a Verma module to a subalgebra of Levi type

We observe that the restriction of a Verma module over a semi-simple Lie algebra to a subalgebra of Levi type may be viewed as a projective functor. By simple arguments we prove that this restriction can be decomposed into a direct sum of standard indecomposables in the category O. For the restriction problem from sl(n+1) to gl(n) we describe the complete answer. We study the properties of the modules with Verma flag also and prove that any module with Verma flag is a submodule of some projective.