Endoscopie et conjecture raffin\'ee de Gan-Gross-Prasad pour les groupes unitaires

TL;DR

This paper proves the local Gan-Gross-Prasad conjecture for tempered representations of unitary groups over p-adic fields, linking branching laws to epsilon factors under endoscopic assumptions.

Contribution

It establishes the conjecture for unitary groups using endoscopic techniques, advancing understanding of representation restrictions in p-adic settings.

Findings

Proves the conjecture for tempered representations of unitary groups.

Shows branching laws can be computed via epsilon factors.

Uses endoscopic assumptions about L-packets.

Abstract

Under endoscopic assumptions about $L$-packets of unitary groups, we prove the local Gan-Gross-Prasad conjecture for tempered representations of unitary groups over $p$-adic fields. Roughly, this conjecture says that branching laws for $U(n-1)\subset U(n)$ can be computed using epsilon factors.