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5 - Complete reducibility and subgroups of exceptional algebraic groups

Published online by Cambridge University Press:  21 November 2024

Edited by
C. M. Campbell ,
M. R. Quick ,
E. F. Robertson ,
C. M. Roney-Dougal  and
D. I. Stewart
C. M. Campbell
Affiliation:
University of St Andrews, Scotland
M. R. Quick
Affiliation:
University of St Andrews, Scotland
E. F. Robertson
Affiliation:
University of St Andrews, Scotland
C. M. Roney-Dougal
Affiliation:
University of St Andrews, Scotland
D. I. Stewart
Affiliation:
University of Manchester
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Summary

This survey article has two components. The first part gives a gentle introduction to Serres notion of $G$-complete reducibility, where $G$ is a connected reductive algebraic group defined over an algebraically closed field. The second part concerns consequences of this theory when $G$ is simple of exceptional type, specifically its role in elucidating the subgroup structure of $G$. The latter subject has a history going back about sixty years. We give an overview of what is known, up to the present day. We also take the opportunity to offer several corrections to the literature.

Keywords

algebraic groupexceptional groupcomplete reducibility
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Groups St Andrews 2022 in Newcastle , pp. 191 - 245
Publisher: Cambridge University Press
Print publication year: 2024

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