Structures immobilières pour un groupe de Kac-Moody sur un corps local (version préliminaire)

Cyril Charignon (1)

1 IECN - Institut Élie Cartan de Nancy

We want to study a Kac-Moody group G over a local field the same way Bruhat and Tits did for reductive groups. We thus want to define somme topological space on which G would act which would as much as possible look like an affine building. It seems to be impossible to really get a building, the spaces we get will be called "hovels" (masures). The present paper aims at generality as it studies in fact a class of groups a bit more general than the Kac-Moody groups, split or quasi split, over a local field: groups with valuated root datum. The hovels we will get will look like the Polygonal (or Satake) compactification of an affine building, rather than like the affine building itself. This way we will get in its border some real affine buildings, corresponding to the parabolic subgroups of G which are reductive. The union of these buildings has been studied before, with the name of "microaffine building".

Domaines: Théorie des groupes [math.GR]

Cyril Charignon. Structures immobilières pour un groupe de Kac-Moody sur un corps local (version préliminaire). 2009. ⟨hal-00438095v2⟩