Remark 3
Tag 01GK, permanent. Cite it as [Bourbaki, Tag 01GK].
Lie Groups and Lie Algebras, chapter IX, § 7. Irreducible representations of connected compact Lie groups
We can deduce Th. 2 from the analogous infinitesimal statement (Chap. VIII, §9, no. 1, Th. 1); the same is true for Th. 3 of the next number (which is the analogue of Th. 2 of loc. cit., no. 2).
Bourbaki sets the proof directly after the statement, and the corpus does not separate them, so what is above is the statement and its proof together.
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