TABLE OF CONTENTS: Acknowledgments xi
Chapter 1: Introduction 1
Chapter 2: A preview 5
Chapter 3: Invariants and reducibility 14
Chapter 4: Diagrammatic notation 27
Chapter 5: Recouplings 42
Chapter 6: Permutations 49
Chapter 7: Casimir operators 60
Chapter 8: Group integrals 76
Chapter 9: Unitary groups 82
Chapter 10: Orthogonal groups 118
Chapter 11: Spinors 132
Chapter 12: Symplectic groups 148
Chapter 13: Negative dimensions 151
Chapter 14: Spinors' symplectic sisters 155
Chapter 15: SU(n) family of invariance groups 162
Chapter 16: G2 family of invariance groups 170
Chapter 17: E8 family of invariance groups 180
Chapter 18: E6 family of invariance groups 190
Chapter 19: F4 family of invariance groups 210
Chapter 20: E7 family and its negative-dimensional cousins 218
Chapter 21: Exceptional magic 229
Epilogue 235
Appendix A.Recursive decomposition 237
Appendix B.Properties of Young projections 239
H. Elvang and P. Cvitanovi´c
B.1 Uniqueness of Young projection operators 239
B.2 Orthogonality 240
B.3 Normalization and completeness 240
B.4 Dimension formula 241
Bibliography 243
Index 259
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