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?
Thanks in advance.