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The maximal subgroups of classical algebraic groups

About this Title

Gary M. Seitz

Publication: Memoirs of the American Mathematical Society
Publication Year: 1987; Volume 67, Number 365
ISBNs: 978-0-8218-2427-6 (print); 978-1-4704-0781-0 (online)
DOI: https://doi.org/10.1090/memo/0365
MathSciNet review: 888704
MSC: Primary 20G15; Secondary 20E28, 20G05

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Table of Contents

Chapters

  • 0. Introduction
  • 1. Preliminary lemmas
  • 2. $Q$-levels and commutator spaces
  • 3. Embeddings of parabolic subgroups
  • 4. The maximal rank theorem
  • 5. The classical module theorem
  • 6. Modules with 1-dimensional weight spaces
  • 7. The rank 1 theorem
  • 8. Natural embeddings of classical groups
  • 9. Component restrictions
  • 10. $V|X$ is usually basic
  • 11. $X = A_n$
  • 12. $X = B_n$, $C_n$, $D_n$, $n \neq 2$
  • 13. $X = B_2$, $C_2$, and $G_2$
  • 14. $X = F_4$ ($p>2$), $E_6$, $E_7$, $E_8$
  • 15. Exceptional cases for $p = 2$ or $3$
  • 16. Embeddings and prime restrictions
  • 17. The main theorems