Twisted Gan-Gross-Prasad conjecture for certain tempered L-packets

TL;DR

This paper explores specific cases of the twisted Gan-Gross-Prasad conjecture for tempered representations, utilizing the theta correspondence to establish new results in the context of unitary groups.

Contribution

It provides new proofs for particular instances of the conjecture when the L-parameter is a sum of conjugate-dual characters, advancing understanding in this area.

Findings

Established special cases of the twisted GGP conjecture

Applied theta correspondence to analyze tempered representations

Identified conditions on L-parameters for the conjecture to hold

Abstract

In this paper, we investigate the twisted GGP conjecture for certain tempered representations using the theta correspondence and establish some special cases, namely when the L-parameter of the unitary group is the sum of conjugate-dual characters of the appropriate sign.