University of Cambridge > Talks.cam > Junior Algebra/Logic/Number Theory seminar > A brief introduction to algebraic groups: their subgroup structure and representation theory

A brief introduction to algebraic groups: their subgroup structure and representation theory

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If you have a question about this talk, please contact Julian Brough.

We will briefly describe the basics of algebraic group theory, when studied over algebraically closed fields. We will survey some important results concerning their subgroup structure, including Liebeck-Seitz’s Theorem on maximal subgroups of the exceptional algebraic groups in positive characteristic. The representation theory of algebraic groups is particularly nice and we will show how all irreducible modules can be described using Steinberg’s Tensor Product Theorem. The motivation behind this is to be able to talk about $G$-irreducible subgroups of exceptional algebraic groups and in particular the speaker’s recent work on them. Time permitting, some of these results will be discussed and the background of the problem.

This talk is part of the Junior Algebra/Logic/Number Theory seminar series.

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