A Local Trace Formula and the Multiplicity One Theorem for the Ginzburg-Rallis Model

Abstract

Following the method developed by Waldspurger and Beuzart-Plessis in their proof of the local Gan-Gross-Prasad conjecture, we are able to prove a local trace formula for the Ginzburg-Rallis model. Then by applying that trace formula, we prove a multiplicity formula for the Ginzburg-Rallis model for tempered representations. Using that multiplicity formula, we prove the multiplicity one theorem for all tempered L-packets. In some cases, we also proved the epsilon dichotomy conjecture which gives a relation between the multiplicity and the exterior cube epsilon factor. Finally, in the archimedean case, we proved some partial results for the general generic representations by applying the open orbit method.