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.

36 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