James Arthur

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In these notes, we shall attempt to make sense of the notions of semisimple and unipotent representations in the context of automorphic forms. Our goal is to formulate some conjectures, both local and global, which were originally motivated by the trace formula. Some of these conjectures were stated less generally in lectures [2] at the University of(More)
We shall outline a classification [A] of the automorphic representations of special orthogonal and symplectic groups in terms of those of general linear groups. This necessarily includes a classification of local L-packets of representations. It also requires a classification of the extended packets that are the local constituents of nontempered automorphic(More)
Preface Following the explicit instructions of the organizers, I have tried to write an article that is suitable for a general mathematical audience. It contains some analogies and metaphors that might even be put to nonmathematicians. I hope that experts will be tolerant of the inevitable simplifications. The principle of functoriality is one of the(More)
Introduction Suppose that G is a semisimple Lie group and that F is a discrete subgroup of G. We assume that F is an arithmetic subgroup defined by congruence conditions , and for simplicity, suppose also that G is contained in a simply connected complex group. A fundamental problem is to decompose the regular representation of G on L2(f\G) into irreducible(More)