# reducible representation

If \(\rho\) is a group representation of a group \(G\) on \(V\), then it is reducible if there is a subspace \(W \subset V\) such that for all \(w\in W\) and all \(g\in G\), \(\rho(g)w \in W\).

That is, if we just restricted our attention to \(W\), we would have a vector space where \(\rho\) is a representation of \(G\).