Structures immobilières pour un groupe de Kac-Moody sur un corps local

Details Structures immobilières pour un groupe de Kac-Moody sur un corps local Structures immobilières pour un groupe de Kac-Moody sur un corps local

2009-12-02

arxiv.org/abs/0912.0442v3

Mathematics

Group Theory

Scientific paper

In this study, we try to generalize Bruhat-Tits's theory to the case of a Kac-Moody group, that is to define an affine building for a Kac-Moody group over a local field. Actually, we will obtain a geometric space wich lacks some of the incidence properties of a building, so that it is called a hovel, following Guy Rousseau's terminology. Hovels have already been obtained for split Kac-Moody groups by Guy Rousseau and St\'ephane Gaussent; here we define them for any group with a (generalized) valuated root datum, a situation wich contains the Kac-Moody groups over local fields, split and nearly split.

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