Image des opérateurs dʼentrelacements normalisés et pôles des séries dʼEisenstein

AbstractThis paper is about the pole of some Eisenstein series for classical groups over a number field. In a previous paper, we have shown how to normalize intertwining operators in such a way that they are holomorphic for positive parameters. Here we show that the image of such operators is (in the interesting cases) either 0 or an irreducible representation. This enables us to compute explicitly the residue of the Eisenstein series obtained from square integrable cohomological representations. At the end of the paper we give necessary and sufficient conditions in terms of Arthurʼs data in order that a square integrable cohomological representation is cuspidal; the conditions are not totally satisfactory and we explain what we expect when Arthurʼs results will be fully available