On endoscopic transfer of Deligne-Lusztig functions

Details On endoscopic transfer of Deligne-Lusztig functions On endoscopic transfer of Deligne-Lusztig functions

2009-02-19

arxiv.org/abs/0902.3426v1

Mathematics

Representation Theory

45 pages

Scientific paper

In this paper we prove the fundamental lemma for Deligne-Lusztig functions. Namely, for every Deligne-Lusztig function $\phi$ on a $p$-adic group $G$ we write down an explicit linear combination $\phi^H$ of Deligne-Lusztig functions on an endoscopic group $H$ such that $\phi$ and $\phi^H$ 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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