In mathematics, specifically in the representation theory of groups and algebras, an irreducible representation ( ρ ρ , V ) or irrep of an algebraic structure A is a nonzero representation that has no proper nontrivial subrepresentation ( ρ ρ | W , W ) , with W ⊂ ⊂ V closed under the action of { ρ ρ ( a ) : a ∈ ∈ A } .