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About: Subrepresentation     Goto   Sponge   NotDistinct   Permalink

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In representation theory, a subrepresentation of a representation of a group G is a representation such that W is a vector subspace of V and . A finite-dimensional representation always contains a nonzero subrepresentation that is irreducible, the fact seen by induction on dimension. This fact is generally false for infinite-dimensional representations. If is a representation of G, then there is the trivial subrepresentation: