Hall polynomials for symplectic groups

CHAPTER PAGE
1 PRELIMINARIES AND MAIN THEOREMS 1
1.1 Introduction 1
1.2 Notation and Definitions 3
1.3 Unipotent classes in G F 5
1.4 The quadric Q 6
1.5 The main theorems 10
1.5.1 Theorem 1.1 10
1.5.2 Theorem 1.2 15
1.5.3 Theorem 1.3 22
1.5.4 Theorem 1.4 28
2 THE CASE OF ONE BLOCK 30
2.1 General remarks 30
2.2 A = l d 32
2.3 X = 2 d 32
2.3.1 Discussion of a Frobenius map 34
2.4 X = r d ,r>2 37
2.5 A closed formula for polynomials g^(q) 38
3 THE GENERAL CASE 41
3.1 Example 41
3.2 Some more notation 43
3.3 Compositions in 1-belt 47
3.4 Compositions in 2-belt 55
3.4.1 Discussion of a Frobenius map 56
3.5 Compositions in &-belt 62
3.6 The general case 71
3.6.1 Compositions in (l,0)-belt 71
3.6.2 Compositions in (2, l)-belt 72
3.6.3 Compositions in (k, k — ^)-belt 74
CITED LITERATURE 77
VITA 78