Corollary
Tag 01GA, permanent. Cite it as [Bourbaki, Tag 01GA].
Lie Groups and Lie Algebras, chapter IX, § 7. Irreducible representations of connected compact Lie groups
The restriction map is bijective.
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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Cites
Nothing.