English

Strongly transitive actions on Euclidean buildings

Metric Geometry 2015-10-27 v2 Group Theory

Abstract

We prove a decomposition result for a group GG 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 XX be a Euclidean building without cone factors. If a group GG of automorphisms of XX acts strongly transitively on the spherical building at infinity X\partial X, then the GG-stabilizer of every affine apartment in XX contains all reflections along thick walls. In particular GG acts strongly transitively on XX if XX is simplicial and thick.

Keywords

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

R2 v1 2026-06-22T09:51:39.827Z