• DOI:10.24033/ASENS.2236
• Corpus ID: 119688839

Local integrability results in harmonic analysis on reductive groups in large positive characteristic

@article{Cluckers2011LocalIR,
  title={Local integrability results in harmonic analysis on reductive groups in large positive characteristic},
  author={Raf Cluckers and Julia Gordon and Immanuel Halupczok},
  journal={arXiv: Representation Theory},
  year={2011}
}

• R. Cluckers, J. Gordon, Immanuel Halupczok
• Published 30 November 2011
• Mathematics
• arXiv: Representation Theory

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 [R. Cluckers, J. Gordon, I. Halupczok, "Transfer principles for integrability and boundedness conditions for motivic exponential functions", preprint arXiv:1111.4405], 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 on the existence of the mock exponential map, 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.