Image des opérateurs d'entrelacements normalisés et pôles des séries d'Eisenstein

Colette Moeglin (1)

1 IMJ - Institut de Mathématiques de Jussieu

We have shown in a preceeding paper how to normalize intertwining operators for classical groups using the twisted endoscopy lifting. In this paper, we prove that the image of such an operator in the cases interesting in the theory of Eisenstein Series, is either 0 or an irreducible representation. As a consequence we compute explicitly the points where Eisenstein Series for square integrable representations are not holomorphic under some hypothesis at the archimedean places: at that places we mainly assume that the infinitesimal character is integral and regular.

Mots clés: opérateurs d'entrelacement; séries d'Eisenstein; formes automorphes de carré intégrable

Domaines: Théorie des représentations [math.RT]; Théorie des nombres [math.NT]

Colette Moeglin. Image des opérateurs d'entrelacements normalisés et pôles des séries d'Eisenstein. 2009. ⟨hal-00398009⟩