Remark 1

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

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

Let S satisfy the condition in Prop. 2 (i), and let $\mathfrak{h}'=s(\mathfrak{h})$ ; denote by $s^*$ the isomorphism $\lambda \rightarrow \lambda \circ s^{-1}$ from $\mathfrak{h}^*$ to $\mathfrak{h}^{'*}$ . It is clear that

S(V^{\lambda}) = V^{s^*\lambda}

In particular:

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. 2