Ebook: Mirrors and Reflections

Mirrors and Reflections presents an intuitive and elementary introduction to finite reflection groups. Starting with basic principles, this book provides a comprehensive classification of the various types of finite reflection groups and describes their underlying geometric properties.

Unique to this text is its emphasis on the intuitive geometric aspects of the theory of reflection groups, making the subject more accessible to the novice. Primarily self-contained, necessary geometric concepts are introduced and explained. Principally designed for coursework, this book is saturated with exercises and examples of varying degrees of difficulty. An appendix offers hints for solving the most difficult problems. Wherever possible, concepts are presented with pictures and diagrams intentionally drawn for easy reproduction.

Finite reflection groups is a topic of great interest to many pure and applied mathematicians. Often considered a cornerstone of modern algebra and geometry, an understanding of finite reflection groups is of great value to students of pure or applied mathematics. Requiring only a modest knowledge of linear algebra and group theory, this book is intended for teachers and students of mathematics at the advanced undergraduate and graduate levels.

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.