Une remarque sur le degre formel d'une serie discrete d'un groupe lineaire general p-adique

Decomposition spectrale et representations speciales d'un groupe reductif p-adique

Let G be a reductive connected p-adic group. With help of the Fourier inversion formula used in [Une formule de Plancherel pour l'algebre de Hecke d'un groupe reductif p-adique - V. Heiermann, Comm. Math. Helv. 76, 388-415, 2001] we give a spectral decomposition on G. In particular we deduce from it essentially that a cuspidal representation of a Levi subgroup M is in the cuspidal support of a square integrable representation of G, if and only if it is a pole of Harish-Chandra's μ-function of order equal to the parabolic rank of M. This result has been conjectured by A. Silberger in 1978. In m…