A linear subspace W ⊂ ⊂ V is called G -invariant if ρ ρ ( g ) w ∈ ∈ W for all g ∈ ∈ G and all w ∈ ∈ W . The co-restriction of ρ ρ to the general linear group of a G -invariant subspace W ⊂ ⊂ V is known as a subrepresentation. A representation ρ ρ : G → → G L ( V ) is said to be irreducible if it has only trivial subrepresentations (all representations can form a subrepresentation with the trivial G -invariant subspaces, e.g. the whole vector space V , and {0}). If there is a proper nontrivial invariant subspace, ρ ρ is said to be reducible.