Let $G$ be a simple simply connected algebraic group defined over an algebraically closed field $K$ and $V$ an irreducible module defined over $K$ on which $G$ acts. Let $E$ denote the set of vectors in $V$ which are ...

This thesis is concerned with three distinct, but closely related, research topics focusing on the unipotent elements of a connected reductive algebraic group G, over an algebraically closed field k, and nilpotent elements ...