G-Complete Reducibility, Geometric Invariant Theory and Spherical Buildings

The authors Michael Bate, Benjamin Martin and Gerhard Röhrle have a longstanding collaboration and friendship (20 years and counting). Together they have written 20 papers in and around this subject area, with a lasting impact on the field of algebraic groups (including subgroup structure, representation theory, geometric invariant theory, spherical buildings) and applications to other areas such as metric geometry and number theory.

• Chapter 1. Introduction.- Chapter 2. Preliminaries.- Chapter 3. Geometric invariant theory.- Chapter 4. G-complete reducibility: first definitions and properties .- Chapter 5. The geometric approach.- Chapter 6. Finiteness, rationality and rigidity results .- Chapter 7. The spherical building of G .- 162 Chapter 8. The optimality formalism.- Chapter 9. Applications to G-complete reducibility .- Chapter 10. Large versus small characteristic .- Chapter 11. G-complete reducibility over an arbitrary field .- Chapter 12.Chapter 12. Variations, applications and future directions .- Chapter 13. Solutions to Exercises.- Bibiliography.- Index.