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Representation Theory

Published by the American Mathematical Society since 1997, this electronic-only journal is devoted to research in representation theory and seeks to maintain a high standard for exposition as well as for mathematical content. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.71.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Virtual transfer factors
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by Julia Gordon and Thomas C. Hales
Represent. Theory 7 (2003), 81-100
Published electronically: March 3, 2003


The Langlands-Shelstad transfer factor is a function defined on some reductive groups over a $p$-adic field. Near the origin of the group, it may be viewed as a function on the Lie algebra. For classical groups, its values have the form $q^c \mathrm {sign}$, where $\mathrm {sign}\in \{-1,0,1\}$, $q$ is the cardinality of the residue field, and $c$ is a rational number. The $\mathrm {sign}$ function partitions the Lie algebra into three subsets. This article shows that this partition into three subsets is independent of the $p$-adic field in the following sense. We define three universal objects (virtual sets in the sense of Quine) such that for any $p$-adic field $F$ of sufficiently large residue characteristic, the $F$-points of these three virtual sets form the partition.

The theory of arithmetic motivic integration associates a virtual Chow motive with each of the three virtual sets. The construction in this article achieves the first step in a long program to determine the (still conjectural) virtual Chow motives that control the behavior of orbital integrals.

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Bibliographic Information
  • Julia Gordon
  • Affiliation: The Fields Institute, 222 College St., Toronto, Ontario, M5T 3J1, Canada
  • Email:
  • Thomas C. Hales
  • Affiliation: Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260
  • Email:
  • Received by editor(s): December 6, 2002
  • Published electronically: March 3, 2003
  • © Copyright 2003 Julia Gordon and Thomas C. Hales
  • Journal: Represent. Theory 7 (2003), 81-100
  • MSC (2000): Primary 11F85, 22E50
  • DOI:
  • MathSciNet review: 1973368