A LOCAL LANGLANDS PARAMETERIZATION FOR GENERIC SUPERCUSPIDAL REPRESENTATIONS OF p-ADIC G2

- We construct a Langlands parameterization of supercuspidal representations of G2 over a p-adic field. More precisely, for any finite extension K/Qp we will construct a bijection .Cg :A & DEG;g(G2, K)-> g & DEG;(G2, K) from the set of generic supercuspidal representations of G2(K) to the set of irreducible continuous homomorphisms p : WK > G2(C) with WK the Weil group of K. The construction of the map is simply a matter of assembling arguments that are already in the literature, together with a previously unpublished theorem of G. Savin on exceptional theta correspondences, included as an appendix. The proof that the map is a bijection is arithmetic in nature, and specifically uses automorphy lifting theorems. These can be applied thanks to a recent result of Hundley and Liu on automorphic descent from GL(7) to G2.