Reflections on concrete buildings
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)].
scientific article; zbMATH DE number 4057803