Structure of α-Stratified Modules for Finite-Dimensional Lie Algebras, I Original Research Article

For complex simple finite-dimensional Lie algebras we study the structure of generalized Verma modules which are torsion free with respect to some subalgebra isomorphic tosl(2). We obtain a criterion of irreducibility and establish necessary and sufficient conditions for the existence of a non-trivial homomorphism between such modules generalizing the BGG theorem for Verma modules.