  In this thesis, we study the Casselman-Jacquet functor. We discuss a new
technical approach which makes the Casselman-Jacquet functor right adjoint to
the Bernstein functor. We give an explanation, using D-modules, of the Bruhat
filtration appearing on the module obtained by applying the Casselman-Jacquet
functor to a principal series representation. We record some conjectures.
