Groupes de Kac-Moody déployés sur un corps local, II Masures ordonnées

Guy Rousseau (1)

1 IECN - Institut Élie Cartan de Nancy

For a split Kac-Moody group (in J. Tits' definition) over a field endowed with a real valuation, we build an ordered affine hovel on which the group acts. This construction generalizes the one already done by S. Gaussent and the author when the residue field contains the complex field [Annales Fourier, 58 (2008), 2605-2657] and the one by F. Bruhat and J. Tits when the group is reductive. We prove that this hovel has all properties of ordered affine hovels (masures affines ordonnées) as defined in [Rousseau, ArXiv 0810.4241]. We use the maximal Kac-Moody group as defined by O. Mathieu and we prove a few new results about it over any field; in particular we prove, in some cases, a simplicity result for this group.

Mots clés: groupe de Kac-Moody; corps valué; immeuble; masure

Domaines: Théorie des groupes [math.GR]

Guy Rousseau. Groupes de Kac-Moody déployés sur un corps local, II Masures ordonnées. 2010. ⟨hal-00512853v1⟩