Lecture 8, MTH 204A (Section B)

We talk about decomposition of actions and representations of groups into irreducible ones. We first introduce the notion of 'irreducibility' of an action. We show that every action can be decomposed into irreducible subactions in a unique way, namely subactions on the orbits under the given action.

Next we talk about irreducibility of representations. We finish the lecture with the proof of Maschke's theorem on complete reducibility of finite dimensional representations of finite groups.