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arXiv · 1710.07881

Scale and tidy subgroups for Weyl-transitive automorphism groups of buildings

Udo Baumgartner·James Parkinson·Jacqui Ramagge
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Abstract

We consider closed, Weyl-transitive groups of automorphisms of thick buildings. For each element of such a group, we derive a combinatorial formula for its scale and establish the existence of a tidy subgroup for it that equals the stabilizer of a simplex. Simplices whose stabilizers are tidy for some element of the group are characterized in terms of the minimal set of the isometry induced by the element on the Davis-realisation of the building and in terms of the Weyl-distance between them and their image. We use our results to derive some topological properties of closed, Weyl-transitive groups of automorphisms.

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Udo Baumgartner, James Parkinson, Jacqui Ramagge. 2017-10-22. Scale and tidy subgroups for Weyl-transitive automorphism groups of buildings. https://arxiv.org/abs/1710.07881

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