For a cuspidal automorphic representation Π of GL(4, A), H. Kim proved that the exterior square transfer ∧Π is nearly an isobaric automorphic representation of GL(6, A). In this paper we characterize those representations Π for which ∧Π is cuspidal.

We complete the work of Cogdell and Piatetski-Shapiro [3] to prove, for n ≥ 3, a converse theorem for automorphic representations of GLn over a number field, with analytic data from twists by unramified representations of GLn−1.

To everyone who loves mathematics, everywhere. i Acknowledgements I cannot stress enough how wonderful it is to study mathematics at Berkeley. I had the great privilege to share ideas there with many fantastic mathematicians. My advisor, Ken Ribet, granted me the freedom to pursue this project while masterfully answering the lion's share of my questions. The ideas for the final chapter grew out...

We study automorphic Lie algebras and their applications to integrable systems. Automorphic are a natural generalisation of celebrated Kac-Moody the case when group automorphisms is not cyclic. They infinite dimensional almost graded. formulate concept graded isomorphism classify s l ( 2 , C ) based corresponding all finite reduction groups. show that hierarchies systems, Lax representations ma...

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1. In this note, we shall describe a classification for automorphic representations of GSp(4), the group of similitudes of four-dimensional symplectic space. The results are part of a project [A3] on the automorphic representations of general classical groups. The monograph [A3] is still in preparation. When complete, it will contain a larger classification of representations, subject to a gene...

There are two kinds of L-functions, and they will be described below: motivic L-functions which generalize the Artin L-functions and are defined purely arithmetically, and automorphic L-functions, defined by data which are largely transcendental. Within the automorphic L-functions a special class can be singled out, the class of standard L-functions, which generalize the Hecke L-functions and f...