  Using principal series Harish-Chandra modules, local cohomology with support
in Schubert cells and twisting functors we construct certain modules
parametrized by the Weyl group and a highest weight in the subcategory O of the
category of representations of a complex semisimple Lie algebra. These are in a
sense modules between a Verma module and its dual. We prove that the three
different approaches lead to the same modules. Moreover, we demonstrate that
they possess natural Jantzen type filtrations with corresponding sum formulae.
