Subrepresentations and Irreducible Representations
As noted earlier, a representation ρ defines an action on a vector space Cn. It may turn out that Cn has an invariant subspace V ⊂ Cn. The action of G is given by complex matrices and this in turn defines a new representation σ : G → GL(V). We call σ a subrepresentation of ρ. A representation without subrepresentations is called irreducible.
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