Motivic functions, integrability, and applications to harmonic analysis on $p$-adic groups

Raf Cluckers; Julia Gordon; Immanuel Halupczok

doi:10.3934/era.2014.21.137

Article Contents

2014, Volume 21: 137-152. Doi: 10.3934/era.2014.21.137

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Motivic functions, integrability, and applications to harmonic analysis on $p$-adic groups

1.
Université Lille 1, Laboratoire Painlevé, CNRS - UMR 8524, Cité Scientifique, 59655 Villeneuve d'Ascq Cedex
2.
Dept. of Mathematics, University of British Columbia, Vancouver BC V6T 1Z2
3.
School of Mathematics, University of Leeds, Woodhouse Lane, Leeds LS2 9JT

Received: August 31, 2013

Revised: July 31, 2014

Published: January 2014

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Abstract

We provide a short and self-contained overview of the techniques based on motivic integration as they are applied in harmonic analysis on $p$-adic groups; our target audience is mainly representation theorists with no background in model theory (and model theorists with an interest in recent applications of motivic integration in representation theory, though we do not provide any representation theory background). We aim to give a fairly comprehensive survey of the results in harmonic analysis that were proved by such techniques in the last ten years, with emphasis on the most recent techniques and applications from [13], [8], and [32, Appendix B].

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Mathematics Subject Classification: 22D12 (03C98).

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