Kirillov theory for compact p-adic groups

Abstract

The purpose here is to describe a method by which one may obtain a reasonably explicit and “global” picture of the unitary representation theory of compact p-adic groups, and to indicate some applications. (By p-adic, we refer to Qpor local fields of characteristic zero.) The basic inspiration for such a description goes back to Kirillov’s work on nilpotent lie groups. The main ingredients are the exponential map and the co-adjoint action. The Campbell-Hausdorff formula is used heavily as a tool. © 1977, University of California, Berkeley. All Rights Reserved.