Lemma 6

Tag 014A, permanent. Cite it as [Bourbaki, Tag 014A].

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

If $\lambda \in P_{++}$ , then ch[ $\lambda ]\in \mathbf{Z}[P]^W$ . The unique maximal term of ch[ $\lambda ]$ (Chap. VI, §3, no. 2, Def. 1) is $e^{\lambda}$ .

The first assertion follows from no. 1, Cor. 2 of Prop. 2, and the second from §6, no. 1, Prop. 1 (ii).

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

Theorem 2, § 7

Cites

Chap. VI, §3, no. 2, Def. 1 not in this corpus
§6, no. 1, Prop. 1
Prop. 2
no. 1, Cor. 2