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A STABLE TRACE FORMULA. I. GENERAL EXPANSIONS

Published online by Cambridge University Press:  24 January 2003

James Arthur
James Arthur
Affiliation:
Department of Mathematics, University of Toronto, Toronto, ON, Canada
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Abstract

This is the first of three articles designed to stabilize the global trace formula. The results apply to any group for which the fundamental lemma (and its variants for weighted orbital integrals) is valid. The main purpose of this paper is to establish a series of expansions that are parallel to the expansions in the trace formula. We shall also formulate the local and global theorems required to interpret the terms in these expansions. The proofs of the theorems will be given in the subsequent two articles. The expansions of this paper will then yield both a stable trace formula, and a decomposition of the ordinary trace formula into a linear combination of stable trace formulae.

AMS 2000 Mathematics subject classification: Primary 22E55. Secondary 11R39

Keywords

automorphic representationstrace formula(weighted) orbital integrals(weighted) charactersstable conjugacytransfer
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 1 , Issue 2 , April 2002 , pp. 175 - 277
Copyright
2002 Cambridge University Press

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