Definition:Irreducible (Representation Theory)/Linear Representation

Definition
Let $\rho: G \to \GL V$ be a linear representation.

Then $\rho$ is irreducible it is not reducible.

That is, there exists no non-trivial proper vector subspace $W$ of $V$ such that:
 * $\forall g \in G: \map {\map \rho g} W \subseteq W$