Remark 1

Tag 01CG, permanent. Cite it as [Bourbaki, Tag 01CG].

Lie Groups and Lie Algebras, chapter IX, § 4. Root system associated to a compact group

The group $W^H_G(T)$ is also the stabilizer in $W_G(T)$ of the subgroup C(H) of T: this follows from Prop. 8 of no. 4.

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.

Cited by

Nothing.

Cites

Prop. 8