Strongly transitive actions on Euclidean buildings
Metric Geometry
2015-10-27 v2 Group Theory
Abstract
We prove a decomposition result for a group acting strongly transitively on the Tits boundary of a Euclidean building. As an application we provide a local to global result for discrete Euclidean buildings, which generalizes results in the locally compact case by Caprace--Ciobotaru and Burger--Mozes. Let be a Euclidean building without cone factors. If a group of automorphisms of acts strongly transitively on the spherical building at infinity , then the -stabilizer of every affine apartment in contains all reflections along thick walls. In particular acts strongly transitively on if is simplicial and thick.
Cite
@article{arxiv.1506.03594,
title = {Strongly transitive actions on Euclidean buildings},
author = {Linus Kramer and Jeroen Schillewaert},
journal= {arXiv preprint arXiv:1506.03594},
year = {2015}
}
Comments
Will appear in Israel Journal of Mathematics