Contents

Chapters in this book

1. Frontmatter i
2. Contents vii
3. Acknowledgments xi
4. Chapter One. Introduction 1
5. Chapter Two. A preview 5
6. Chapter Three. Invariants and reducibility 14
7. Chapter Four. Diagrammatic notation 27
8. Chapter Five. Recouplings 42
9. Chapter Six. Permutations 49
10. Chapter Seven. Casimir operators 60
11. Chapter Eight. Group integrals 76
12. Chapter Nine. Unitary groups 82
13. Chapter Ten. Orthogonal groups 118
14. Chapter Eleven. Spinors 132
15. Chapter Twelve. Symplectic groups 148
16. Chapter Thirteen. Negative dimensions 151
17. Chapter Fourteen. Spinors’ symplectic sisters 155
18. Chapter Fifteen. SU(n) family of invariance groups 162
19. Chapter Sixteen. G2 family of invariance groups 170
20. Chapter Seventeen. E8 family of invariance groups 180
21. Chapter Eighteen. E6 family of invariance groups 190
22. Chapter Nineteen. F4 family of invariance groups 210
23. Chapter Twenty. E7 family and its negative-dimensional cousins 218
24. Chapter Twenty-One. Exceptional magic 229
25. Appendix A. Recursive decomposition 237
26. Appendix B. Properties of Young projections 239
27. Bibliography 243
28. Index 259