Irreducible representations

Let \rho:G\to \text{GL}(V) be a linear representation of G. We say that it is irreducible or simple if V is not 0 and if no vector subspace of V is stable under G, except of course 0 and V. This is equivalent to saying V is not the direct sum of two representations, except for the trivial decomposition V=0\oplus V.

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