Strongly transitive actions on Euclidean buildings

2015/06/11 by Kramer, Linus, Schillewaert, Jeroen
#FOS: Mathematics #Group Theory (math.GR) #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1506.03594

Abstract

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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