Reflection Groups and Invariant Theory

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ISBN: 978-1-4419-3194-8 (Print) 978-1-4757-3542-0 (Online)

Table of contents (35 chapters)

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  1. Front Matter

    Pages i-ix

  2. Introduction

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      Book Chapter

      Pages 1-3

      Introduction: Reflection groups and invariant theory

  3. Reflection groups

    1. Front Matter

      Pages 5-5

    2. No Access

      Book Chapter

      Pages 6-24

      Euclidean reflection groups

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      Book Chapter

      Pages 25-34

      Root systems

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      Book Chapter

      Pages 35-44

      Fundamental systems

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      Book Chapter

      Pages 45-56

      Length

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      Book Chapter

      Pages 57-63

      Parabolic subgroups

  4. Coxeter groups

    1. Front Matter

      Pages 65-65

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      Book Chapter

      Pages 66-74

      Reflection groups and Coxeter systems

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      Book Chapter

      Pages 75-80

      Bilinear forms of Coxeter systems

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      Book Chapter

      Pages 81-96

      Classification of Coxeter systems and reflection groups

  5. Weyl groups

    1. Front Matter

      Pages 97-97

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      Book Chapter

      Pages 98-108

      Weyl groups

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      Book Chapter

      Pages 109-117

      The Classification of crystallographic root systems

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      Book Chapter

      Pages 118-134

      Affine Weyl groups

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      Book Chapter

      Pages 135-143

      Subroot systems

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      Book Chapter

      Pages 144-151

      Formal identities

  6. Pseudo-reflection groups

    1. Front Matter

      Pages 153-153

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      Book Chapter

      Pages 154-160

      Pseudo-reflections

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      Book Chapter

      Pages 161-167

      Classifications of pseudo-reflection groups

  7. Rings of invariants

    1. Front Matter

      Pages 169-169

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      Book Chapter

      Pages 170-179

      The ring of invariants

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      Book Chapter

      Pages 180-190

      Poincaré series

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      Book Chapter

      Pages 191-201

      Nonmodular invariants of pseudo-reflection groups

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      Book Chapter

      Pages 202-211

      Modular invariants of pseudo-reflection groups

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