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- James Arthur, Robert Kottwitz
- 1989

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)

- James Arthur
- 2012

- James Arthur
- 2006

- JAMES ARTHUR
- 2002

- JAMES ARTHUR
- 1988

are obtained by integrating f with respect to the invariant measure on the conjugacy class of y. They are of considerable importance for the harmonic analysis of G(F). Invariant orbital integrals are also of interest because they occur on the geometric side of the trace formula, in the case of compact quotient. For the general trace formula, the analogous… (More)

- James Arthur
- 2005

Introduction The trace formula for GL2 has yielded a number of deep results on automorphic forms. The same results ought to hold for general groups, but so far, little progress has been made. One of the reasons has been the lack of a suitable trace formula. In [l(d)] and [l(e)] we presented a formula or, as we wrote it in [l(e), $51, G is a reductive group… (More)

- JAMES ARTHUR
- 2002

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)

- James Arthur
- 2005

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)

- JAMES ARTHUR
- 1985

- James Arthur, Toronto
- 1994