Remark 2
Tag 01GJ, permanent. Cite it as [Bourbaki, Tag 01GJ].
Lie Groups and Lie Algebras, chapter IX, § 7. Irreducible representations of connected compact Lie groups
Similarly, the first equality of Cor. 4 remains valid without the assumption that .
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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Nothing.