Endoscopic Classification of Representations of GSp(2n) and GSO(2n)

In 1989 Arthur conjectured a very precise description about the structure of automorphic representations of reductive groups using Arthur packets and endoscopy theory. In his recent monograph [Art13], he proved this conjecture for symplectic groups and orthogonal groups G. The results are conditional on the stabilization of twisted trace formula, which is a project in progress under Moeglin and Waldspurger (see [MW14], [Wal14a]-[Wal14e]). Our goal is to extend Arthur's result to general symplectic groups and general even orthogonal groups eG, by studying the restriction of representations from $\tilde{G}$ to G. This idea goes back to Labesse and Langlands [LL79], where they considered G to be SL(2) and $\tilde{G}$ to be GL(2).To extend Arthur's result, there are two main problems that we have solved in this thesis. One is local and the other is global. Locally, we have determined the tempered Arthur packets for $\tilde{G}$, and shown they satisfy certain character relations under the endoscopic transfer. Globally, we have proven the functoriality of endoscopic transfer for a large family of tempered automorphic representations of $\tilde{G}$.Ph.D