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