University of Birmingham > Talks@bham > Algebra Seminar > Complete reducibility in exceptional algebraic groups: the good, the bad and the ugly

Complete reducibility in exceptional algebraic groups: the good, the bad and the ugly

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The notion of complete reducibility was introduced by J. P. Serre in 1998. It generalises the notion of a completely reducible module in classical representation theory. After giving an introduction to complete reducibility for algebraic groups, we discuss its impact on questions about the subgroup structure of exceptional algebraic groups. This includes recent and ongoing work with A. Litterick on classifying the subgroups of exceptional algebraic groups that are not completely reducible. The techniques used are a mix of standard representation theory, non-abelian cohomology and computational group theory.

This talk is part of the Algebra Seminar series.

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