Definition:Reducible Linear Representation

Definition
Let $\rho: G\to \operatorname{GL}\left(V\right)$ be a linear representation

$\rho$ is reducible iff there exists $W$ a proper subspace of $V$ such that $\rho(g)(W)\subset W$. This means that $W$ is invariant for all $\rho(g)$ where $g\in G$

It is called irreducible iff it is not reducible.