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

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.

arXiv comment36 pages. We have substantially revised Section 5. We now first use parabolic reduction to reduce to the good parity case, then combine endoscopic reduction with further parabolic reduction to reduce to small-rank cases, where we can use theta correspondence reducing to known cases