On Casselman-Wallach globalization theorem
Seminar Room 1, Newton Institute
About 20 years ago B.Casselman and N.Wallach proved a remarkable theorem about representations of real reductive groups. Namely they proved that any Harish Chandra module $M$ for a group $G$ can be uniquely extended to a smooth Frechet representation $V$ of this group (they called this procedure "the canonical globalization").
Unfortunately their proof is quite involved. For this reason their result is not that well known as it should be. For the same reason some natural generalizations of this result (e.g. how to make such globalization in a family) could not be studied.
In my lecture I will describe a new approach to this problem developed in a joint work by B. Kroetz and myself that is technically simpler and allows to investigate some related phenomena.