On proving the Casselman-Wallach globalization theorem

Abstract

The recent proof of the Casselman-Wallach globalization theorem by J. Bernstein and B. Krötz is studied. Some parts are emphasized, while others are not treated in full detail. For certain parts where the original article \cite{KB} was not completely clear to us, more details are provided. In particular, more attention is given to proving that minimal principal series representations are good, and emphasis is placed on our new definition of these Harish-Chandra modules being of D-type.