  Recently we have started a program to describe the action of Lie algebras
associated with Dynkin-type diagrams on generic Verma modules in terms of
polynomial vector fields. In this paper we explain that the results for the
classical ABCD series of Lie algebras coincide with the more conventional
approach, based on the knowledge of the entire algebra, not only the simple
roots. We apply the coset description, starting with a large representation and
then reducing it with the help of the algebra, commuting with the original one.
The irreducible representations are then obtained by gauge fixing this residual
symmetry.
