Mirrors and Reflections

• Main Authors: Borovik, Alexandre V. (Author), Borovik, Anna. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: New York, NY : Springer New York, 2010.
• Series: Universitext
• Subjects: Mathematics.; Group theory.; Matrix theory.; Topological Groups.; Geometry.; Mathematical physics.; Group Theory and Generalizations.; Topological Groups, Lie Groups.; Linear and Multilinear Algebras, Matrix Theory.; Mathematical Methods in Physics.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-0-387-79066-4

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 thi...

Table of Contents:

• Part I Geometric Background
• 1. Affine Euclidean Space ARn
• 2 Isometries of ARn
• 3 Hyperplane Arrangements
• 4 Polyhedral Cones
• 5 Mirrors and Reflections
• 6 Systems of Mirrors
• 7 Dihedral Groups
• 8 Root Systems
• 9 Root Systems AnŁ1, BCn, Dn
• 10 Chambers
• 11 Generation
• 12 Coxeter Complex
• 13 Residues
• 14 Generalized Permutahedra
• Part IV Classification
• 15 Generators and Relations
• 16 Classification of Finite Reflection Groups
• 17 Construction of Root Systems
• 18 Orders of Reflection Groups
• Part V Three-Dimensional Reflection Groups
• 19 Reflection Groups in Three Dimensions
• 20 Icosahedron
• Part VI Appendices
• References
• Index.