Proposition 18

Tag 01K9, permanent. Cite it as [Bourbaki, Tag 01K9].

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

The group Aut(G) $/$ Int(G) is isomorphic to Aut(D) $/W(D)$ .

In particular, assume that G is semi-simple; the group Aut(D) can then be identified with the subgroup of $A(R(G,T))$ (Chap. VI, §1, no. 1) consisting of the elements $u$ such that $u(X(T))\subset X(T)$ , and the subgroup W(D) can be identified with $W(R(G,T))$ .

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

Chap. VI, §1, no. 1