Corollary 1

Tag 013L, permanent. Cite it as [Bourbaki, Tag 013L].

Lie Groups and Lie Algebras, chapter VIII, § 7. Finite dimensional modules over a split semi-simple Lie algebra

If $\lambda \in \mathscr{X}$ and $\lambda (H_{\alpha})\geq 1$ , then $\lambda -\alpha \in \mathscr{X}$ . If $\lambda +\alpha \in \mathscr{X}$ and $\lambda (H_{\alpha}) = 0$ , then $\lambda \in \mathscr{X}$ and $\lambda -\alpha \in \mathscr{X}$ .

This follows immediately from Prop. 3 (i).

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. 3