CUBIC CORRESPONDENCES ARISING FROM G(2)

We use the automorphic realization of the minimal representation (the theta representation) of the three fold cover of Gz to construct a cor respondence of automorphic forms between members of dual pairs inside G(2). The dual pairs under consideration are (SL(2), SL(2)) and (SL(3) , Z(3)). In the first case, we obtain the Shimura correspondence betwe en the threefold cover of SL(2) and SL(2), through explicit integral f ormulae. In the second case, we decompose theta over the three fold co ver of SL(3), both locally and globally. The constituents are parametr ized by their central characters and are cuspidal, except (essentially ) when the central character is trivial. We thus obtain ''cuspidal the ta representations'' and ''the unramified theta representation'' of th e three fold cover of SL(3).