Mirrors and Reflections

• Main Authors: Borovik, Alexandre V. (Author), Borovik, Anna (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: New York, NY : Springer New York, 2010.
• Series: Universitext
• Subjects: Mathematics.; Algebra.; Group theory.; Matrix theory.; Topological groups.; Lie groups.; Geometry.; Physics.; Group Theory and Generalizations.; Topological Groups, Lie Groups.; Linear and Multilinear Algebras, Matrix Theory.; Mathematical Methods in Physics.

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:

• Geometric Background
• Affine Euclidean Space
• Isometries of
• Hyperplane Arrangements
• Polyhedral Cones
• Mirrors, Reflections, Roots
• Mirrors and Reflections
• Systems of Mirrors
• Dihedral Groups
• Root Systems
• Root Systems An?1, BCn, Dn
• Coxeter Complexes
• Chambers
• Generation
• Coxeter Complex
• Residues
• Generalized Permutahedra
• Classification
• Generators and Relations
• Classification of Finite Reflection Groups
• Construction of Root Systems
• Orders of Reflection Groups
• Three-Dimensional Reflection Groups
• Reflection Groups in Three Dimensions
• Icosahedron.