Corollary 1

Tag 015B, permanent. Cite it as [Bourbaki, Tag 015B].

Lie Groups and Lie Algebras, chapter VIII, § 8. Symmetric invariants

Assume that $\mathfrak{g}$ is simple. Let $m_1, . . . , m_l$ be the exponents of the Weyl group of $\mathfrak{g}$ . There exist elements $P_1, . . . ,P_l$ of $I(\mathfrak{g}^*)$ , homogeneous of degrees

m_1+ 1, . . . , m_l+ 1

which are algebraically independent and generate the algebra $I(\mathfrak{g}^*)$ .

This follows from Th. 2 (i) and Chap. V, §6, no. 2, Prop. 3.

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

Exercise 11, § 11

Cites

Chap. V, §6, no. 2, Prop. 3 not in this corpus
Th. 2