Stability of the smooth Casselman-Jacquet functor

Abstract

We establish and prove several results for the smooth Casselman-Jacquet submodule and quotient functors for real reductive groups. Other than exactness, surjectivity and globalization results, we establish a stability on the intersection of Jacquet subspaces. As an application, we establish a full version of the real Bernstein-Zelevinsky filtrations for smooth Fréchet representations of moderate growth rate.