Lectures in mathematics : Kyoto University
vol. 12
Theory of group characters / by Richard Brauer ; notes prepared by T. Tsuzuku in cooperation with T. Nakayama ... [et al.]
c1979
I. Preliminaries | |
§ 1. Algebras and their representations | 1-8 |
§ 2. Representations of finite groups - classical theory | 8-19 |
§ 3. Cyclotomic splitting fields | 19-30 |
II. Arithmetical Structure | |
§ 1. The numbers ω_i(K_α) | 31 |
§ 2. Modular representations and their characters | 32-33 |
§ 3. Transition from an ordinary representation to a modular one | 33-34 |
§ 4. Decomposition numbers and Cartan invariants | 34-37 |
§ 5. The number of irreducible modular characters | 37-39 |
§ 6. The chacacters φ_ρ | 39-41 |
§ 7. The p-rank of the matrix D of decomposition numbers | 41-43 |
§ 8. Blocks | 43-46 |
§ 9. Idempotents belonging to blocks | 46-50 |
§ 10. Defect of a block | 50-52 |
§ 11. The determinant of the matrix C of Cartan invariants | 52-56 |
§ 12. The elementary divisors of C and C_τ | 56-63 |
§ 13. The number of irreducible characters in a block | 63-66 |
III. Defect groups. Main theorem A | |
§ 1. Blocks of G and those of subgroups | 67-71 |
§ 2. Defect groups of a block | 71-78 |
§ 3. Main Theorem A | 78-81 |
IV. Generalized Decomposition Numbers, Main Theorem B | |
§ 1. Generalized decomposition numbers | 82-84 |
§ 2. Sections | 84-88 |
§ 3. The matrix of generalized decomposition numbers | 88-92 |
§ 4. Main Theorem B | 93 |
§ 5. Some consequences | 93-104 |
References | 104-107 |