Irreducible representation

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

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