In this paper we determine the structure of the full lift for the Howe correspondence of $(Sp(n),O(V))$ for rank-one reducibilities.

In this note we show that for an arbitrary reductive Lie group and any admissible irreducible Banach representation the Mellin transforms of Whittaker functions extend to meromorphic functions. We locate the possible poles and show that they always lie along translates of walls of Weyl chambers.

An irreducible supercuspidal representation $\pi$ of $G= \GL(n,F)$, where $F$ is a nonarchimedean local field of characteristic zero, is said to be ``distinguished'' by a subgroup $H$ of $G$ and a quasicharacter $\chi$ of $H$ if $\Hom_H(\pi,\chi)\noteq 0$. There is a suitable global analogue of this notion for and irreducible, automorphic, cuspidal representation associated to $\GL(n)$. Under certain general hypotheses, it is shown in this paper that every distinguished, irreducible, supercuspidal representation may be realized as a local component of a distinguished, irreducible automorphic, cuspidal representation. Applications to the theory of distinguished supercuspidal representations are provided.

James Arthur was awarded the Canada Gold Medal of the National Science and Engineering Research Council in 1999. This introduction to his work is an attempt to explain his methods and his goals to the mathematical community at large.

It is shown that given a local $L$-function defined by Langlands-Shahidi method, there exists a highly ramified character of the group which when is twisted with the original representation leads to a trivial $L$-function.

Let $H$ be an exceptional, adjoint group of type $E_6$ and split rank 2, over a $p$-adic field $k$. In this article we discuss the restriction of the minimal representation of $H$ to a dual pair $\PD^{\times}\times G_2(k)$, where $D$ is a division algebra of dimension 9 over $k$. In particular, we discover an interesting class of supercuspidal representations of $G_2(k)$.

Let $H$ be the split, adjoint group of type $E_6$ over a $p$-adic field. In this paper we study the restriction of the minimal representation of $H$ to the closed subgroup $PGL_3 \times G_2$.