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Invariant Theory

About this Title

Mara D. Neusel, Texas Tech University, Lubbock, TX

Publication: The Student Mathematical Library
Publication Year 2007: Volume 36
ISBNs: 978-0-8218-4132-7 (print); 978-1-4704-2147-2 (online)
DOI: http://dx.doi.org/10.1090/stml/036
MathSciNet review: MR2280491
MSC: Primary 13A50; Secondary 20C05, 20C30, 20C40

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Table of Contents

Front/Back Matter

• View this volume's front and back matter

Chapters

• 1. Introduction

Part 1. Recollections

• Chapter 1. Linear representations of finite groups
• Chapter 2. Rings and algebras

Part 2. Introduction and Göbel’s bound

• Chapter 3. Rings of polynomial invariants
• Chapter 4. Permutation representations
• Application: Decay of a spinless particle
• Application: Counting weighted graphs

Part 3. The first fundamental theorem of invariant theory and Noether’s bound

• Chapter 5. Construction of invariants
• Chapter 6. Noether’s bound
• Chapter 7. Some families of invariants
• Application: Production of fibre composites
• Application: Gaussian quadrature

Part 4. Noether’s theorems

• Chapter 8. Modules
• Chapter 9. Integral dependence and the Krull relations
• Chapter 10. Noether’s theorems
• Application: Self-dual codes

Part 5. Advanced counting methods and the Shephard-Todd-Chevalley theorem

• Chapter 11. Poincaré series
• Chapter 12. Systems of parameters
• Chapter 13. Pseudoreflection representations
• Application: Counting partitions
• Appendix A. Rational invariants

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