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Representations and subgroup structure of simple algebraic groups

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Building on the fundamental work of Dynkin for the complex semisimple Lie algebras, numerous mathematicians have studied the restrictions of irreducible representations of simple algebraic groups to closed subgroups. We will give an overview of the work carried out since 1985, starting with Seitz’s major contribution in the late 80s. In particular, this work illustrates the connection between the study of such restrictions and the determination of the maximal closed connected subgroups of the classical type algebraic groups.

We describe the classification of the irreducible actions of all maximal positive-dimensional closed subgroups of simple algebraic groups and highlight some interesting branching rules for non irreducible actions. This includes work of Burness, Ford, Ghandour, Marion and Cavallin.

This talk is part of the Groups St Andrews 2017 series.

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