La formule du caractère des représentations associées à une orbite fermée

Abstract

Let π be a unitary irreducible representation of almost connected solvable p-adic group G (p≠2) and Ω the attached coadjoint orbit according to Duflo's orbit method. We suppose Ω is closed. Then the representation is admissible and we prove a character formula expressing in some neighborhoods of each semi-simple element s of G the character of π in terms of the Fourier transform of the Liouville measure on the set of s-fixed points in Ω. As a by-product we establish in Maktouf (2012) [14] a character formula in the general case and derive the description of the Plancherel formula.