Le groupe fondamental de certains espaces d'orbites regulieres de groupes de Weyl affines

The affine Weyl group W _aof an irreducible root system of rank n acts on the complexification h of a real space of dimension n via the usual (affine) action on the imaginary part and the action through the finite Weyl group on the real part. This group acts freely on the complement h of some complex hyperplanes. We prove a presentation of the fundamental group of the quotient hW _a.

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A Jacques Tits pour son soixantième anniversaire