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A sketchy proof of this theorem is proposed in Sect.
We refer to [114] for a sketchy proof, let us just observe that if we have a continuous family of finite dimensional representations, the multiplicity of an irreducible summand is a locally constant function on the parameter space T (being given by the scalar product of the respective trace functions, it is an integer valued continuous function, hence locally constant).
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com