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