On unitarizability in the case of classical p-adic groups

In the introduction of this paper we discuss a possible approach to the unitarizability problem for classical p-adic groups. In this paper we give some very limited support that such approach is not without chance. In a forthcoming paper we shall give additional evidence in generalized cuspidal rank (up to) three.Comment: This paper is a merged and revised version of ealier preprints arXiv:1701.07658 and arXiv:1701.07662. The paper is going to appear in the Proceedings of the Simons Symposium on Geometric Aspects of the Trace Formul

Global Jacquet-Langlands correspondence, multiplicity one and classification of automorphic representations

In this paper we show a local Jacquet-Langlands correspondence for all unitary irreducible representations. We prove the global Jacquet-Langlands correspondence in characteristic zero. As consequences we obtain the multiplicity one and strong multiplicity one theorems for inner forms of GL(n) as well as a classification of the residual spectrum and automorphic representations in analogy with results proved by Moeglin-Waldspurger and Jacquet-Shalika for GL(n).Comment: 49 pages; Appendix by N. Grba

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