Masures affines

Guy Rousseau (1)

1 IECN - Institut Élie Cartan de Nancy

We give an abstract definition of affine hovels which generalizes the definition of affine buildings (eventually non simplicial) given by Jacques Tits and includes the hovels built by Stephane Gaussent and the author for some Kac-Moody groups over ultrametric fields. We prove that, in such an affine hovel I, there exist retractions with center a sector germ and that we can add at the infinity of I a pair of twin buildings or two microaffine buildings. For some affine hovels I, we prove that the residue at a point of I has a natural structure of pair of twin buildings and that there exists on I a preorder which induces on each apartment the preorder associated to the Tits cone.

Mots clés: groupe de Kac-Moody; immeuble affine

Domaines: Théorie des groupes [math.GR]; Géométrie métrique [math.MG]

Guy Rousseau. Masures affines. Pure and Applied Mathematics Quarterly, 2011, 7 (3), pp.859-921. ⟨hal-00333401⟩