Example 2

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

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

If G and $G'$ are two connected compact Lie groups, with maximal tori T and $T'$ , respectively, and if $D^*(G,T) = (M,M_0,R)$ and $D^*(G',T') =$ $(M',M'_0,R')$ , then $D^*(G\times G',T\times T')$ can be identified with $(M\oplus M',M_0\oplus$ $M'_0,R\cup R')$ . Similarly for the covariant diagrams.

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.