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Abstract: This 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. [Copyright &y& Elsevier]

Abstract: For or , isomorphism classes of irreducible -modules for are parametrized by n-dimensional representations of the Weil group of F. We can induce to a representation of , which has index 2 in . That gives a process of “automorphic induction” which to an irreducible -module τ for associates an irreducible -module for . In the present paper we show that if τ is unitary and generic then π is determined by τ, up to isomorphism, via a character identity entirely analogous to the character identity occurring in the automorphic induction process for p-adic fields. This completes the theory of automorphic induction for local and global representations of over number fields. [Copyright &y& Elsevier]