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arXiv · 1312.5541

Transitive parallelism of residues in buildings

Antoine Clais
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Abstract

We study the buildings in which parallelism of residues is an equivalence relation. If the building admits a group action, we describe how parallel residues are related to residues with equal stabilizers. This permits to retrieve the fact that in a Coxeter group or in a graph product, intersections of parabolic subgroups are parabolic.

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Antoine Clais. 2016-06-28. Transitive parallelism of residues in buildings. https://arxiv.org/abs/1312.5541

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