Abstract

In this talk, we first give an elementary introduction to nilpotent orbits in semisimple Lie algebras. Then we briefly talk about how to relate the nilpotent orbits to representations of semisimple Lie groups. This is part of the philosophy of nilpotent orbits (in a very loose sense). Finally, we present some recent work on the orbit philosophy. We aim at demonstrating this by giving examples on some small groups.