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arXiv · 0902.3426

On endoscopic transfer of Deligne-Lusztig functions

David Kazhdan·Yakov Varshavsky
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Abstract

In this paper we prove the fundamental lemma for Deligne-Lusztig functions. Namely, for every Deligne-Lusztig function $ϕ$ on a $p$-adic group $G$ we write down an explicit linear combination $ϕ^H$ of Deligne-Lusztig functions on an endoscopic group $H$ such that $ϕ$ and $ϕ^H$ have ``matching orbital integrals''. In particular, we prove a conjecture of Kottwitz. More precisely, we do it under some mild restriction on $p$.

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David Kazhdan, Yakov Varshavsky. 2009-02-19. On endoscopic transfer of Deligne-Lusztig functions. https://doi.org/10.1215/00127094-1548371

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