Symmetries, Lie Algebras and Representations : A Graduate Course for Physicists (Hardcover)

Preface; 1. Symmetries and conservation laws; 2. Basic examples; 3. The Lie algebra su(3) and hadron symmetries; 4. Formalization: algebras and Lie algebras; 5. Representations; 6. The Cartan-Weyl basis; 7. Simple and affine Lie algebras; 8. Real Lie algebras and real forms; 9. Lie groups; 10. Symmetries of the root system. The Weyl group; 11. Automorphisms of Lie algebras; 12. Loop algebras and central extensions; 13. Highest weight representations; 14. Verma modules, Casimirs, and the character formula; 15. Tensor products of representations; 16. Clebsch-Gordan coefficients and tensor operators; 17. Invariant tensors; 18. Subalgebras and branching rules; 19. Young tableaux and the symmetric group; 20. Spinors, Clifford algebras, and supersymmetry; 21. Representations on function spaces; 22. Hopf algebras and representation rings; Epilogue; References; Index.