# Supercuspidals : clarification

A supercuspidal representation is an admissible representation with trivial Jacquet module for any parabolic.This implies that the matrix coeff. are compactly supported mod center.

Cartier (in Corivalis) defines super cuspidal rep as admissible rep. with compactly supported matrix coeff. mod center.

I am wondering if this (Cartier's) definition is equivalent to triviality of Jacquet module? If yes, is there a reference for such a proof?

It is funny how, when you read papers from the 1970s or 1980s on p-adic groups, they always quote this book as "the soon to be published book", and yet, we are in 2011 and this book is still unpublished! –  M Turgeon Oct 13 '11 at 0:59