Image des op\'erateurs d'entrelacements normalis\'es et p\^oles des s\'eries d'Eisenstein

TL;DR

This paper investigates normalized intertwining operators for classical groups, demonstrating their images are either zero or irreducible, and explicitly identifying non-holomorphic points of Eisenstein series under certain conditions.

Contribution

It proves the irreducibility or nullity of intertwining operator images in key cases and explicitly computes non-holomorphic points of Eisenstein series for square integrable representations.

Findings

Images of intertwining operators are either 0 or irreducible.

Explicit determination of non-holomorphic points of Eisenstein series.

Assumption of integral and regular infinitesimal character at archimedean places.

Abstract

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.