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

2017/10/22 by Baumgartner, Udo, Parkinson, James, Ramagge, Jacqui · 2 citations
#20E36 #20F65 #22D05 #52E24 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1710.07881

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.

Cited by

• On flat groups in affine buildings
• Describing the nub in maximal Kac-Moody groups

Related

• Rigidity of the group topology for closed Weyl transitive groups of automorphisms of a regular locally finite building
• On the Howe--Moore property for automorphism groups of buildings
• Strongly transitive actions on Euclidean buildings
• Contraction Groups and Passage to Subgroups and Quotients for Endomorphisms of Totally Disconnected Locally Compact Groups
• Uniclass automorphisms of spherical buildings