Mirrors and Reflections: The Geometry of Finite Reflection Groups [Paperback]

This graduate/advanced undergraduate textbook contains a systematic and elementary treatment of finite groups generated by reflections. The approach is based on fundamental geometric considerations in Coxeter complexes, and emphasizes the intuitive geometric aspects of the theory of reflection groups. Key features include: many important concepts in the proofs are illustrated in simple drawings, which give easy access to the theory; a large number of exercises at various levels of difficulty; some Euclidean geometry is included along with the theory of convex polyhedra; no prerequisites are necessary beyond the basic concepts of linear algebra and group theory; and a good index and bibliography The exposition is directed at advanced undergraduates and first-year graduate students.

Starting with basic principles, this book provides a comprehensive classification of the various types of finite reflection groups and describes their underlying geometric properties. Numerous exercises at various levels of difficulty are included.

Mirrors and Reflections is a systematic and elementary treatment of finite groups generated by reflections. The approach is based on fundamental geometric considerations in Coxeter complexes, and emphasizes the intuitive geometric aspects of the theory of reflection groups.

Key features: Many important concepts in the proofs are illustrated in simple drawings, which give easy access to the theory  A large number of exercises at various levels of difficulty  Some Euclidean geometry is included along with the theory of convex polyhedra  Few prerequisites are necessary beyond linear algebra and the basic notions of group theory.

The exposition is directed at advanced undergraduates and first-year graduate students.