Reflections on concrete buildings
type: Item
instance of: scholarly article
title: Reflections on concrete buildings
zbMATH Open document ID: 0648.20051
DOI: 10.1007/BF00191924
author: William M. Kantor
published in: Geometriae Dedicata
publication date: 1988-01-01T00:00:00Z
review text: Let \(\Delta\) be the affine building of an algebraic simple group over a locally compact local field and let G be a discrete automorphism group of \(\Delta\) which acts transitively on at least one of the types of vertices of \(\Delta\). Here the author assumes that \(\Delta\) is associated to an orthogonal group and that G is generated by reflections in hyperplanes perpendicular to certain nonsingular vectors. If these vectors are suitably chosen it is easy to see that the corresponding group G has the properties mentioned above. This new approach yields many of the known examples of groups G. In a second part of the paper the classification of groups G which are even chamber-transitive is described, these groups have already been determined by the author, \textit{R. A. Liebler} and \textit{J. Tits} [Bull. Am. Math. Soc., New Ser. 16, 129-133 (1987; Zbl 0631.20033)].
Mathematics Subject Classification ID: 20G25
Mathematics Subject Classification ID: 20H15
Mathematics Subject Classification ID: 51F15
Mathematics Subject Classification ID: 20E36
Mathematics Subject Classification ID: 51J05
zbMATH DE Number: 4057803
zbMATH Keywords: affine building
zbMATH Keywords: algebraic simple group
zbMATH Keywords: locally compact local field
zbMATH Keywords: discrete automorphism group
zbMATH Keywords: orthogonal group
zbMATH Keywords: generated by reflections
zbMATH Keywords: chamber-transitive
reviewed by: Norbert Knarr
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf00191924
OpenAlex ID: W4213378051
description: scientific article; zbMATH DE number 4057803