Postdoctoral Math Seminar

I will try to do the following, on the example of SL_2 (R): Talk about the Casselman-Jacquet module - a basic tool in the representation theory of real groups encoding asymptotics of matrix coefficients. Perform an analytic calculation of the Casselman-Jacquet module of a principal series representation. Explain, in brief, how one passes from the analytic setting to an algebraic one, and then to an (algebro-)geometric one. Indicate how to redo the analytic calculation above in this latter setting.