Irreducible Subgroups of Exceptional Algebraic Groups Seminar

A subgroup of a semisimple algebraic group $G$ is said to be $G$-irreducible if it lies in no proper parabolic subgroup of $G$. A result of Liebeck and Testerman shows that connected $G$-irreducible subgroups are nearly maximal and therefore interesting to study. Work of Stewart, Amende and Liebeck-Seitz gives some partial results on simple connected $G$-irreducible subgroups for $G$ an exceptional algebraic group.

I will discuss recent work I have done in classifying all connected $G$-irreducible subgroups, up to conjugacy, in all characteristics. This classification gives us the 'lattice' structure of the connected $G$-irreducible subgroups. I will also discuss some corollaries of this structure as well as future work.