Title: The basic theory of (Ug,K)-modules
Speaker: Professor Matthew Emerton
Speaker Info: Northwestern
Brief Description:
Special Note:
Abstract:
The notion of (Ug,K)-module was introduced by Harish-Chandra as an algebraic and Lie-theoretic tool that could be used to study infinite-dimensional representations of reductive groups. After explaining very briefly how (Ug,K)-modules arise (a point that will be dealt with more fully in a future lecture), I will discuss the basic algebraic properties of these objects. The main goal will be to explain what it means for a (Ug,K)-module to be admissible, and to give several useful equivalent characterisations of admissibility. In the course of doing this, I will state (but not prove!) the celebrated subrepresentation theorem of Casselman.Date: Tuesday, January 29, 2002