La conjecture locale de Gross-Prasad pour les groupes sp\'eciaux orthogonaux: le cas g\'en\'eral

Abstract

We prove the local Gross-Prasad conjecture for generic L-packets of representations of special orthogonal groups. The proof uses the same result for tempered L-packets proved in a preceding paper, and irreducibility results for the induced representations of whose the elements of the L-packets are Langlands quotients.