Example 3

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

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

Let N be a closed subgroup of T, central in G, and let $(M,M_0,R)$ be the contravariant diagram of G relative to T. Then the contravariant diagram of $G/N$ relative to $T/N$ can be identified with $(M',M'_0,R)$ , where $M'$ is the subgroup of M consisting of the $\lambda$ such that $\lambda (N) =\{1\}$ and $M'_0= M'\cap M_0$ .

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

Proposition 16, § 4

Cites

Nothing.