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Representation Theory

ISSN 1088-4165



Good orbital integrals

Authors: Clifton Cunningham and Thomas C. Hales
Journal: Represent. Theory 8 (2004), 414-457
MSC (2000): Primary 22E50, 14F42
Published electronically: September 9, 2004
MathSciNet review: 2084489
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Abstract: 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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Additional Information

Clifton Cunningham
Affiliation: Department of Mathematics, University of Calgary, Alberta, Canada, T2N 1N4

Thomas C. Hales
Affiliation: Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260

Keywords: Orbital integrals, local constancy, motivic integration, Fundamental Lemma
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
Article copyright: © Copyright 2004 C. Cunningham and T. C. Hales