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. In addition to exactness, surjectivity, transitivity and globalization results, we establish a stability property for the intersection of Jacquet subspaces. Our approach is based on a family of seminorms on the Casselman-Jacquet quotient module. As an application, we establish a full version of the real Bernstein-Zelevinsky filtrations for smooth Fréchet representations of moderate growth.

40 pages, v2: reorganized version, 49 pages