Alladi Ramakrishnan Hall

Casselman-Wallach globalisation and its applications

Aprameyan Parthasarathy

University of Paderborn

In this talk, we'll explain briefly the results on globalisations of Harish Chandra-modules due to Casselman and Wallach, and outline the main ideas of the proof. We'll then mention how this has important and interesting consequences such as giving a proof of the Helgason conjecture at the level of distributions, giving
holomorphic extensions of K-finite vectors of admissible Banach representations etc.