| In this thesis, written under the direction of Professor Benedict Gross, we study the liftings of representations or automorphic forms between members of a dual reductive pair in an exceptional group over a finite, local or number field. This lifting, called the theta correspondence, is effected by a distinguished representation of the exceptional group, called the minimal representation, which is an analogue of the Weil representation of the metaplectic group. Over a finite or local field, the lifting is found to respect Langlands' functoriality. Over the rational number field, we construct an automorphic realization of the global minimal representation using Langlands' theory of Eisenstein series, and obtain necessary and sufficient conditions for the theta lift to be a non-zero cusp form. We also take the first step towards obtaining a Siegel-Weil formula for a particular dual pair. |