Contents
Chapter 1. Introduction 1
Acknowledgments 8
Chapter 2. Preliminaries 9
2.1. Notation and terminology 9
2.2. Weights and multiplicities 10
2.3. Tensor products and reducibility 11
2.4. Invariant forms 11
2.5. Connected subgroups 12
2.6. Clifford theory 13
2.7. Parabolic embeddings 14
2.8. Some remarks on the case H = H0.2 17
2.9. Reducible subgroups 18
2.10. Some A1-restrictions 19
Chapter 3. The case H0 = Am 23
3.1. The main result 23
3.2. Preliminaries 24
3.3. Some results on exterior powers 26
3.4. The case H0 = A2 28
3.5. The case H0 = A3 33
3.6. The case H0 = Am, m 4 41
Chapter 4. The case H0 = Dm, m 5 63
4.1. The main result 63
4.2. Preliminaries 63
4.3. The Borel reduction 65
4.4. Proof of Theorem 4.1.1 72
Chapter 5. The case
H0
= E6 77
5.1. The main result 77
5.2. Preliminaries 77
5.3. Proof of Theorem 5.1.1 81
Chapter 6. The case
H0
= D4 87
6.1. The main result 87
6.2. The Borel reduction 87
6.3. The case H = D4.2 91
6.4. The case H = D4.3 94
6.5. The case H = D4.S3 97
iii
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