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The theory of buildings was introduced by J Tits in order to focus on geometric and combinatorial aspects of simple groups of Lie type. Since then the theory has blossomed into an extremely active field of mathematical research having deep connections with topics as diverse as algebraic groups, arithmetic groups, finite simple groups, and finite geometries, as well as with graph theory and other aspects of combinatorics.
This volume is an up-to-date survey of the theory of buildings with special emphasis on its interaction with related geometries. As such it will be an invaluable guide to all those whose research touches on these themes. The articles presented here are by experts in their respective fields and are based on talks given at the 1988 Buildings and Related Geometries conference at Pingree Park, Colorado. Topics covered include the classification and construction of buildings, finite groups
associated with building-like geometries, graphs and association schemes.
List of contents
Mark Ronan: Classification and construction of buildings; Jacques Tits: Spheres of Radius 2 in triangle buildings. I; Stanley E. Payne: A census of finite generalized quadrangles; William M. Kantor: Finite geometries via algebraic affine buildings; Thomas Meixner: Groups acting transitively on locally finite classical Tits chamber systems; Udo Ott: Representation theory of chamber systems of affine type; Michael Aschbacher: The geometry of trilinear forms; Arjeh M. Cohen: Local recognition of graphs, buildings, and related geometries; Richard Weiss: Generalized polygons and s-transitive graphs; Eiichi Bannai: Character tables of commutative association schemes; J.W.P. Hirschfeld: Codes and curves; J.A. Thas: Solution of a classical problem on finite inversive planes
