Towards the Plancherel Formula of GL(2) over a p-adic field

Abstract

This project aims to write down the Plancherel formula for GL(2; F) where F is a p-adic eld. The Plancherel formula for SL(2; F) and PGL(2; F) are known, and we also have a general form of the formula for a real reductive semisimple lie group. Thus, in this project we aim to do the same for GL(2; F). We do not arrive at the nal formula, instead we give an approach to the proof of this formula. This project details all the requirements such as, its irreducible representations and their characters, as well as other possible ways to get to the problem. We hope to solve the problem soon.