Cluckers, R, Gordon, J and Halupczok, I (2014) Local integrability results in harmonic analysis on reductive groups in large positive characteristic. Annales Scientifiques de l’École Normale Supérieure, 47 (6). 6. pp. 1163-1195. ISSN 0012-9593
Abstract
Let G be a connected reductive algebraic group over a non-Archimedean local field K, and let g be its Lie algebra. By a theorem of Harish-Chandra, if K has characteristic zero, the Fourier transforms of orbital integrals are represented on the set of regular elements in g(K) by locally constant functions, which, extended by zero to all of g(K), are locally integrable. In this paper, we prove that these functions are in fact specializations of constructible motivic exponential functions. Combining this with the Transfer Principle for integrability of [8], we obtain that Harish-Chandra's theorem holds also when K is a non-Archimedean local field of sufficiently large positive characteristic. Under the hypothesis that mock exponential map exists, this also implies local integrability of Harish-Chandra characters of admissible representations of G(K), where K is an equicharacteristic field of sufficiently large (depending on the root datum of G) characteristic.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Keywords: | Harish-Chandra characters, orbital integrals, Fourier transforms, local integrability, reductive groups above a local body. |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 27 Feb 2015 15:24 |
Last Modified: | 03 Sep 2019 11:12 |
Published Version: | http://smf4.emath.fr/Publications/AnnalesENS/4_47/... |
Status: | Published |
Publisher: | Societe Mathematique de France |
Identification Number: | 10.24033/asens.2236 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:83361 |