What to read after Group Theory?

Chapter 1. Introduction 1 Chapter 2. A preview 5 2.1 Basic concepts 5 2.2 First example: SU(n) 9 2.3 Second example: E6 family 12 Chapter 3. Invariants and reducibility 14 3.1 Preliminaries 14 3.2 Defining space, tensors, reps 18 3.3 Invariants 19 3.4 Invariance groups 22 3.5 Projection operators 24 3.6 Spectral decomposition 25 Chapter 4. Diagrammatic notation 27 4.1 Birdtracks 27 4.2 Clebsch-Gordan coefficients 29 4.3 Zero- and one-dimensional subspaces 32 4.4 Infinitesimal transformations 32 4.5 Lie algebra 36 4.6 Other forms of Lie algebra commutators 38 4.7 Classification of Lie algebras by their primitive invariants 38 4.8 Irrelevancy of clebsches 39 4.9 A brief history of birdtracks 40 Chapter 5. Recouplings 43 5.1 Couplings and recouplings 43 5.2 Wigner 3n-j coefficients 46 5.3 Wigner-Eckart theorem 47 Chapter 6. Permutations 50 6.1 Symmetrization 50 6.2 Antisymmetrization 52 6.3 Levi-Civita tensor 54 6.4 Determinants 56 6.5 Characteristic equations 58 6.6 Fully (anti)symmetric tensors 58 6.7 Identically vanishing tensors 59 Chapter 7. Casimir operators 61 7.1 Casimirs and Lie algebra 62 7.2 Independent casimirs 63 7.3 Adjoint rep casimirs 65 7.4 Casimir operators 66 7.5 Dynkin indices 67 7.6 Quadratic, cubic casimirs 70 7.7 Quartic casimirs 71 7.8 Sundry relations between quartic casimirs 73 7.9 Dynkin labels 76 Chapter 8. Group integrals 78 8.1 Group integrals for arbitrary reps 79 8.2 Characters 81 8.3 Examples of group integrals 82 Chapter 9. Unitary groups 84 P Cvitanovid, H. Elvang, and A.D. Kennedy 9.1 Two-index tensors 84 9.2 Three-index tensors 85 9.3 Young tableaux 86 9.4 Young projection operators 92 9.5 Reduction of tensor products 96 9.6 U(n) recoupling relations 100 9.7 U(n) 3n-j symbols 101 9.8 SU(n) and the adjoint rep 105 9.9 An application of the negative dimensionality theorem 107 9.10 SU(n) mixed two-index tensors 108 9.11 SU(n) mixed defining @ adjoint tensors 109 9.12 SU(n) two-index adjoint tensors 112 9.13 Casimirs for the fully symmetric reps of SU(n) 117 9.14 SU(n), U(n) equivalence in adjoint rep 118 9.15 Sources 119 Chapter 10. Orthogonal groups 121 10.1 Two-index tensors 122 10.2 Mixed adjoint 0 defining rep tensors 123 10.3 Two-index adjoint tensors 124 10.4 Three-index tensors 128 10.5 Gravity tensors 130 10.6 SO(n) Dynkin labels 133 Chapter 11. Spinors 135 P Cvitanovi6 and A.D. Kennedy 11.1 Spinography 136 11.2 Fierzing around 139 11.3 Fierz coefficients 143 11.4 6-j coefficients 144 11.5 Exemplary evaluations, continued 146 11.6 Invariance of y-matrices 147 11.7 Handedness 148 11.8 Kahane algorithm 149 Chapter 12. Symplectic groups 152 12.1 Two-index tensors 153 Chapter 13. Negative dimensions 155 P Cvitanovid and A.D. Kennedy 13.1 SU(n) = 3U( -n) 156 13.2 SO(n) = Yp( -n) 158 Chapter 14. Spinors' symplectic sisters 160 P Cvitanovid and A.D. Kennedy 14.1 Spinsters 160 14.2 Racah coefficients 165 14.3 Heisenberg algebras 166 Chapter 15. SU(n) family of invariance groups 168 15.1 Reps of SU(2) 168 15.2 SU(3) as invariance group of a cubic invariant 170 15.3 Levi-Civita tensors and SU(n) 173 15.4 SU(4)-SO(6) isomorphism 174 Chapter 16. G2 family of invariance groups 176 16.1 Jacobi relation 178 16.2 Alternativity and reduction of f-contractions 178 16.3 Primitivity implies alternativity 181 16.4 Casimirs for G2 183 16.5 Hurwitz's theorem 184 Chapter 17. E8 family of invariance groups 186 17.1 Two-index tensors 187 17.2 Decomposition of Sym3A 190 17.3 Diophantine conditions 192 17.4 Dynkin labels and Young tableaux for Fe 193 Chapter 18. E6 family of invariance groups 196 18.1 Reduction of two-index tensors 196 18.2 Mixed two-index tensors 198 18.3 Diophantine conditions and the Eý family 199 18.4 Three-index tensors 200 18.5 Defining 0 adjoint tensors 202 18.6 Two-index adjoint tensors 205 18.7 Dynkin labels and Young tableaux for 6 209 18.8 Casimirs for E6 210 18.9 Subgroups of EF 213 18.10 Springer relation 213 18.11 Springer's construction of 4 214 Chapter 19. F4 family of invariance groups 216 19.1 Two-index tensors 19.2 Defining 0 adjoint tensors 216 19.3 Jordan algebra and F4(26) 219 19.4 Dynkin labels and Young tableaux for F4 223 Chapter 20. E7 family and its negative-dimensional cousins 224 20.1 SO(4) family 20.2 Defining ® adjoint tensors 225 20.3 Lie algebra identification 227 20.4 E7 family 228 20.5 Dynkin labels and Young tableaux for E 233 Chapter 21. Exceptional magic 235 21.1 Magic Triangle 235 21.2 A brief history of exceptional magic 238 21.3 Extended supergravities and the Magic Triangle 238 Epilogue 242 Appendix A. Recursive decomposition 244 Appendix B. Properties of Young projections 246 H. Elvang and P Cvitanovid B.1 Uniqueness of Young projection operators B.2 Orthogonality 246 B.3 Normalization and completeness 247 B.4 Dimension formula 247 248.