Israel Journal of Mathematics

, Volume 219, Issue 1, pp 163–170 | Cite as

Strongly transitive actions on euclidean buildings

  • Linus Kramer
  • Jeroen Schillewaert


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


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© Hebrew University of Jerusalem 2017

Authors and Affiliations

  1. 1.Mathematisches InstitutUniversität MünsterMünsterGermany

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