Corollary 4

Tag 0AB8, permanent. Cite it as [Bourbaki, Tag 0AB8].

Lie Groups and Lie Algebras, chapter III, § 3. Passage from a Lie group to its Lie algebra

Let $G$ be a Lie group and $\pi$ an analytic linear representation of $G$ on a finite-dimensional vector space $E$ . Then the representations $T^n(\pi)$ , $S^n(\pi)$ and $\wedge^n(\pi)$ of $G$ (Appendix) are analytic and

L(T^n(\pi)) = T^n(L(\pi)), \quad L(S^n(\pi)) = S^n(L(\pi)), \quad L(\wedge^n(\pi)) = \wedge^n(L(\pi)).

This follows from Corollary 3 and Proposition 40.

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

Cited by

Nothing.

Cites

Proposition 40
Corollary 3