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More About This Textbook
Overview
This book consists of three parts, rather different in level and purpose. The first part was originally written for quantum chemists. It describes the correspondence, due to Frobenius, between linear representations and characters. The second part is a course given in 1966 to second-year students of l’Ecole Normale. It completes in a certain sense the first part. The third part is an introduction to Brauer Theory.
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Table of Contents
Part I: Representations and Characters; 1. Generalities on Linear Representation; 2. Character Theory; 3. Subgroups, products, induced representations; 4. Compact Groups; 5. Examples; Bibliography Part I; Part II: Representation in Characteristic Zero; 6. The Group Algebra; 7. Induced Representations- Mackey's Criterion; 8. Examples of Induced Representations; 9. Artin's Theorem; 10. A Theorem of Brauer; 11. Applications of Brauer's Theorem; 12. Rationality Questions; 13. Rationality Questions: Examples; Bibliography Part II; Part III: Introduction to Brauer Theory; 14. The Groups Rk(G), Rk(G) and Pk(G); 15. The cde Triangle; 16. Theorems; 17. Proofs; 18. Modular Characters; 19. Application to Artin Representations; Appendix; Bibliography part III; Index of Notation; Index of Terminology.