Twisted Gan-Gross-Prasad conjecture for unramified quadratic extensions

TL;DR

This paper proves a significant conjecture in automorphic forms and representation theory using a trace formula approach, specifically addressing the twisted Gan-Gross-Prasad conjecture for unramified quadratic extensions.

Contribution

It establishes the twisted global Gan-Gross-Prasad conjecture for certain unitary groups under unramified and local conditions, advancing the understanding of automorphic periods.

Findings

Proves the conjecture under specified unramified conditions

Utilizes a relative trace formula approach

Refines the conjecture with additional local assumptions

Abstract

Using a relative trace formula approach, we prove the twisted global Gan-Gross-Prasad conjecture for $\operatorname{U}(V) \subseteq \operatorname{GL}(V)$, as well as its refinement, under some unramifiedness assumptions and local conditions on the quadratic extension and the automorphic representation.