Definition 2

Tag 01J6, permanent. Cite it as [Bourbaki, Tag 01J6].

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

A finite dimensional irreducible representation $\rho$ of $\mathfrak g$ is said to be orthogonal (resp. symplectic) if there exists on E a non-degenerate symmetric (resp. alternating) bilinear form invariant under $\rho$ .

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.

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