Finite reflectıon groups<br><br>Second edıtıon<br>l.c. grove<br>c.t. benson<br><br><br><br>CONTENTS<br>CHAPTER 1<br>Preliminaries 1<br>1.1 Linear Algebra 1<br>1.2 Group Theory 3<br>CHAPTER 2<br>Finite Groups in Two and Three Dimensions 5<br>2.1 Orthogonal Transformations in Two Dimensions 5<br>2.2 Finite Groups in Two Dimensions 7<br>2.3 Orthogonal Transformations in Three Dimensions 9<br>2.4 Finite Rotation Groups in Three Dimensions 11<br>2.5 Finite Groups in Three Dimensions 18<br>2.6 Crystallographic Groups 21<br>Exercises 22<br>CHAPTER 3<br>Fundamental Regions 27<br>Exercises 32<br>CHAPTER 4<br>Coxeter Groups 34<br>4.1 Root Systems 34<br>4.2 Fundamental Regions for Coxeter Groups 43<br>Exercises 50<br>ix<br> <br>c<br>CHAPTER 5<br>Classification of Coxeter Groups<br>5.1 Coxeter Graphs<br>5.2 The Crystallographic Condition<br>5.3 Construction of Irreducible Coxeter Groups<br>5.4 Orders of Irreducible Coxeter Groups Exercises<br>CHAPTER 6<br>Generators and Relations for Coxeter Groups Exercises<br>CHAPTER 7<br>Invariants<br>7.1 Introduction<br>7.2 Polynomial Functions<br>7.3 Invariants<br>7.4 The Molien Series Exercises<br>Postlude<br>APPENDIX<br>Crystallographic Point Groups<br>References Index<br>