A new axiomatics for masures
Group Theory
2023-09-13 v3 Representation Theory
Abstract
Masures are generalizations of Bruhat-Tits buildings. They were introduced to study Kac-Moody groups over ultrametric fields, which generalize reductive groups over the same fields. If A and A are two apartments in a building, their intersection is convex (as a subset of the finite dimensional affine space A) and there exists an isomorphism from A to A fixing this intersection. We study this question for masures and prove that the analogous statement is true in some particular cases. We deduce a new axiomatic of masures, simpler than the one given by Rousseau.
Cite
@article{arxiv.1710.09272,
title = {A new axiomatics for masures},
author = {Auguste Hébert},
journal= {arXiv preprint arXiv:1710.09272},
year = {2023}
}
Comments
This paper was initially called "Convexity in a masure"