Geometry of Coxeter groups

Howard Hiller0273085174, 9780273085171

Table of contents :
Title page ……Page 1
Date-line ……Page 2
Contents ……Page 3
Dedication ……Page 4
Preface ……Page 5
INTRODUCTION ……Page 7
CHAPTER I. COXETER GROUPS ……Page 12
§1. Coxeter systems ……Page 13
§2. Tit’s theorem ……Page 23
§3. Root systems ……Page 28
§4. Classification ……Page 37
§5. Parabolic subgroups ……Page 47
§6. Bruhat order ……Page 50
§7. Historical notes ……Page 54
Appendix:Forms ……Page 59
CHAPTER II. INVARIANT THEORY ……Page 63
§1. Finiteness results ……Page 64
§2. Poincare series ……Page 70
§3. Complex reflection groups ……Page 82
§4. Relative invariants ……Page 94
§5. Historical notes ……Page 96
CHAPTER III. GEOMETRY OF GRASSMANNIANS ……Page 102
§1. Preliminaries ……Page 103
§2. Chern classes ……Page 105
§3. Schubert calculus ……Page 113
§4. Flag manifolds ……Page 124
§5. Complements ……Page 133
CHAPTER IV. SCHUBERT CALCULUS OF THE COINVARIANT ALGEBRA ……Page 139
§1. Basis theorem ……Page 140
§2. Giambelli formula ……Page 146
§3. Pieri formula ……Page 153
§4. Parabolic invariants ……Page 158
§5. Geometry of the symmetric group ……Page 161
§6. Complements ……Page 168
CHAPTER V. COMBINATORICS OF THE BRUHAT ORDER ……Page 171
§1. Combinatorics ……Page 172
§2. Miniscule weights ……Page 177
§3. Intersection theory ……Page 181
§4, Seshadri’s standard monomial theory ……Page 189
§5. Complements ……Page 192
§6. Affine Weyl groups ……Page 198
REFERENCES ……Page 208
INDEX ……Page 218