Corollary 1

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

Lie Groups and Lie Algebras, chapter IX, § 7. Irreducible representations of connected compact Lie groups

With the notations of no. 3, we have in $\mathbf{Z}[X(T)]$ ,

$(\sum_{w\in W}\varepsilon (w)e^{w\rho})$ Ch[ $\lambda ] =\sum_{w\in W}\varepsilon (w)e^{w\lambda}e^{w\rho}$ for all $\lambda \in X_{++}$ .

This follows from the theorem and commutative diagram (2) (no. 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.

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