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Mautner's lemmainrepresentation theory, named after Austrian-American mathematician Friederich Mautner, states that if G is a topological group and π a unitary representationofG on a Hilbert space H, then for any xinG, which has conjugates
converging to the identity element e, for a net of elements y, then any vector vofH invariant under all the π(y) is also invariant under π(x).
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