Proposition 30

Tag 0AW6, permanent. Cite it as [Bourbaki, Tag 0AW6].

Lie Groups and Lie Algebras, chapter VI, § 1. Root systems

Assume that $R$ is irreducible. Let $m$ be an integer between 1 and $h - 1$ and prime to $h$ . Then $\exp(\frac{2i\pi m}{h})$ is an eigenvalue of $c$ of multiplicity 1.

In particular, $m$ is an exponent of $W$ , cf. Chap. V, § 6, no. 2.

We first prove a lemma:

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

Cited by

§ 4. Classification of root systems

Cites

Chap. V, § 6, no. 2