Distances on a masure (affine ordered hovel)
Group Theory
2021-08-25 v3 Metric Geometry
Representation Theory
Abstract
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.
Cite
@article{arxiv.1611.06105,
title = {Distances on a masure (affine ordered hovel)},
author = {Auguste Hébert},
journal= {arXiv preprint arXiv:1611.06105},
year = {2021}
}