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Unipotent and Nilpotent Classes in Simple Algebraic Groups and Lie Algebras

About this Title

Martin W. Liebeck, Imperial College of London, London, United Kingdom and Gary M. Seitz, University of Oregon, Eugene, OR

Publication: Mathematical Surveys and Monographs
Publication Year: 2012; Volume 180
ISBNs: 978-0-8218-6920-8 (print); 978-0-8218-8510-9 (online)
DOI: https://doi.org/10.1090/surv/180
MathSciNet review: 2883501
MSC: Primary 20G15; Secondary 17B08

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Table of Contents

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Front/Back Matter

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Chapters

• 1. Introduction
• 2. Preliminaries
• 3. Classical groups in good characteristic
• 4. Classical groups in bad characteristic: Statement of results
• 5. Nilpotent elements: The symplectic and orthogonal cases, $p=2$
• 6. Unipotent elements in symplectic and orthogonal groups, $p=2$
• 7. Finite classical groups
• 8. Tables of examples in low dimensions
• 9. Exceptional groups: Statement of results for nilpotent elements
• 10. Parabolic subgroups and labellings
• 11. Reductive subgroups
• 12. Annihilator spaces of nilpotent elements
• 13. Standard distinguished nilpotent elements
• 14. Exceptional distinguished nilpotent elements
• 15. Nilpotent classes and centralizers in $E_8$
• 16. Nilpotent elements in the other exceptional types
• 17. Exceptional groups: Statement of results for unipotent elements
• 18. Corresponding unipotent and nilpotent elements
• 19. Distinguished unipotent elements
• 20. Non-distinguished unipotent classes
• 21. Proofs of theorems 1, 2 and corollaries 3–8
• 22. Tables of nilpotent and unipotent classes in the exceptional groups