Kirillov theory for compact p-adic groups

Roger Evans Howe

Vol. 73 (1977), No. 2, 365–381

DOI: 10.2140/pjm.1977.73.365

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 Q_p, or 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.

Mathematical Subject Classification 2000

Primary: 22E50

Milestones

Received: 21 May 1977

Published: 1 December 1977