Remark

Tag 0AYJ, permanent. Cite it as [Bourbaki, Tag 0AYJ].

Lie Groups and Lie Algebras, chapter VI, § 4. Classification of root systems

It can be shown that the canonical map

\operatorname{Aut}(\tilde{X}, \tilde{f}) \to \operatorname{Aut}(\Sigma)

is an isomorphism.

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

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