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

Cyril Charignon (1)

1 IECN - Institut Élie Cartan de Nancy

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 Stéphane 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.

Mots clés: groupe; immeuble; corps local; donnée radicielle valuée; Bruhat-Tits; building; local field; valuated root datum

Domaines: Théorie des groupes [math.GR]

Cyril Charignon. Structures immobilières pour un groupe de Kac-Moody sur un corps local. 2010. ⟨hal-00438095v3⟩