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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.


Good orbital integrals
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by Clifton Cunningham and Thomas C. Hales
Represent. Theory 8 (2004), 414-457
Published electronically: September 9, 2004


This paper concerns a class of orbital integrals in Lie algebras over $p$-adic fields. The values of these orbital integrals at the unit element in the Hecke algebra count points on varieties over finite fields. The construction, which is based on motivic integration, works both in characteristic zero and in positive characteristic. As an application, the Fundamental Lemma for this class of integrals is lifted from positive characteristic to characteristic zero. The results are based on a formula for orbital integrals as distributions inflated from orbits in the quotient spaces of the Moy-Prasad filtrations of the Lie algebra. This formula is established by Fourier analysis on these quotient spaces.
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Bibliographic Information
  • Clifton Cunningham
  • Affiliation: Department of Mathematics, University of Calgary, Alberta, Canada, T2N 1N4
  • Email:
  • Thomas C. Hales
  • Affiliation: Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260
  • Email:
  • Received by editor(s): November 21, 2003
  • Received by editor(s) in revised form: April 27, 2004
  • Published electronically: September 9, 2004
  • Additional Notes: The research of the second author was supported in part by the NSF
    This work is licensed under the Creative Commons Attribution License. To view a copy of this license, visit or send a letter to Creative Commons, 559 Nathan Abbott Way, Stanford, California 94305, USA
  • © Copyright 2004 C. Cunningham and T. C. Hales
  • Journal: Represent. Theory 8 (2004), 414-457
  • MSC (2000): Primary 22E50, 14F42
  • DOI:
  • MathSciNet review: 2084489