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I don't know a particular paper to which to point, but, from a harmonic analyst's point of view, it seems to me that Weyl's results on compact Lie groups essentially closed the field of "representation theory of compact Lie groups." (I post this with great trepidation, because this or any answer seems an invitation to someone else to point out in what senses the field proposed is still alive and thriving—but that would be a fun thing to know, too!)