Algebra Seminar

What are the finite subgroups of simple complex Lie groups G which act irreducibly on all fundamental representations of G ?

In this talk, reporting on joint work with K. Magaard and P.H. Tiep, we will show how this question can be solved using two ingredients: the classification of finite simple groups, and Lusztig's theory of characters of reductive groups. With the same methods one can determine those irreducible complex representations of finite simple groups, whose alternating or symmetric square is again irreducible.