Distances on a masure (affine ordered hovel)

Auguste Hébert (1, 2, 3)

1 UJM - Université Jean Monnet - Saint-Étienne
2 Université de Lyon
3 AGL - Algèbre, géométrie, logique

A masure (a.k.a affine ordered hovel) I is a generalization of the Bruhat-Tits building that is associated to a split Kac-Moody group G over a non-archimedean local field. This is a union of affine spaces called apartments. When G is a reductive group, I is a building and there is a G-invariant distance inducing a norm on each apartment. In this paper, we study distances on I inducing the affine topology on each apartment. We show that some properties (completeness, local compactness, ...) cannot be satisfyed when G is not reductive. Nevertheless, we construct distances such that each element of G is a continuous automorphism of I.

Mots clés: Kac-Moody group; masure; hovel; building

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

Auguste Hébert. Distances on a masure (affine ordered hovel). 2018. ⟨hal-01397819v2⟩