A Local Trace Formula for the Local Gross-Prasad Conjecture for Special Orthogonal Groups

Abstract

In this paper, through combining the work of Jean-Loup Waldspurger and Rapha ̈el Beuzart-Plessis, we are going to give a proof for the tempered part of the local Gross-Prasad conjecture for special orthogonal groups over any local fields of characteristic zero, which was previously proved by Waldspurger over p-adic fields. As a crucial ingredient for the proof, we express the germs of Lie algebra orbital integrals associated to the regular nilpotent orbits in a quasi-split connected reductive algebraic group over any local fields of characteristic zero in terms of endoscopic invariants, which extends the work of Diana Shelstad over p-adic fields.