  Let g be a semisimple complex Lie algebra and k in g be any algebraic
subalgebra reductive in g. For any simple finite dimensional k-module V, we
construct simple (g; k)-modules M with finite dimensional k-isotypic components
such that V is a k-submodule of M and the Vogan norm of any simple k-submodule
V' of M; V' not isomorphic to V, is greater than the Vogan norm of V . The (g;
k)-modules M are subquotients of the fundamental series of (g; k)-modules
introduced in [PZ2].
