Automorphic Representations of the Jacobi Group and of Gl 2
نویسنده
چکیده
A lifting map from cuspidal automorphic representations of the Jacobi group G J to cuspidal auto-morphic representations of the group PGL(2) is constructed. The lifting also has a local deenition, and the local and global versions are compatible. The local lifts can be described in terms of equivalence classes of local representations. The main idea in the construction is to exploit the close relationship between representations of G J and of the metaplectic group Mp, and then to make use of Waldspurger's constructions for the metaplectic group. The resulting Jacobi-PGL(2)-lift has some immediate consequences for the automorphic representation theory of the Jacobi group, e.g. for the deenition of automorphic L-functions. When restricted to the classical situation, the constructed lifting coincides with the Skoruppa-Zagier correspondence between classical Jacobi forms and elliptic modular forms in SZ].
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