  We apply the super duality formalism recently developed by the authors to
obtain new equivalences of various module categories of general linear Lie
superalgebras. We establish the correspondence of standard, tilting, and simple
modules, as well as the identification of the u-homology groups, under these
category equivalences. As an application, we obtain a complete solution of the
irreducible character problem for some new parabolic BGG categories of
gl(m|n)-modules, including the full BGG category of gl(m|2)-modules, in terms
of type A Kazhdan-Lusztig polynomials.
