The local Gross-Prasad conjecture over $\mathbb{R}$: Epsilon dichotomy

TL;DR

This paper proves the epsilon dichotomy aspect of the local Gross-Prasad conjecture over the real numbers for tempered local L-parameters, building on Waldspurger's work.

Contribution

It establishes the epsilon dichotomy for the local Gross-Prasad conjecture over  for tempered local L-parameters, extending previous theoretical results.

Findings

Proved the epsilon dichotomy over  for tempered local L-parameters.

Extended Waldspurger's work to the real case.

Contributed to the understanding of the local Gross-Prasad conjecture.

Abstract

Following the work of Jean-Loup Waldspurger, we prove the epsilon dichotomy part of the local Gross-Prasad conjecture over $\mathbb{R}$ for tempered local $L$-parameters.