Adjoint action and nilpotent orbits using representations of quivers

Abstract: 

We will see how categories of representations of quivers and quasi-herediary algebras can be used to study orbits and prehomogeneous spaces arising from the adjoint action of a Lie group on the radical of its Lie algebra. In particular, we will consider Richardsons classical result on the existence of dense orbits for parabolic Lie algebras (due to Brustle-Hille-Ringel-Rohrle), the generalisation of Richardsons theorem to biparabolic Lie algebras in classical types and give a new characterisation of Dynkin graphs using actions of quiver Lie algebras.