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

TL;DR

This paper proves the local Gross-Prasad conjecture for generic L-packets of special orthogonal groups, extending previous results and utilizing irreducibility of induced representations.

Contribution

It establishes the conjecture for the general case of special orthogonal groups, building on prior work for tempered L-packets.

Findings

Proves the local Gross-Prasad conjecture for generic L-packets

Utilizes irreducibility results for induced representations

Extends previous results to the general case

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.