Good filtrations for representations of Lie algebras of Cartan type

AbstractIn this paper we define induced and “Weyl” modules for an infinite-dimensional Hopf algebra D(G)u(g). This algebra is important because its representation theory encompasses the representation theory of a given Lie algebra of Cartan type. A cohomological criterion is provided which states precisely when a D(G)u(g)-module admits a filtration with sections of induced modules or “Weyl” modules