Example 2

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

Lie Groups and Lie Algebras, chapter VI, § 3. Exponential invariants

By Remark 2 of no. 3, we can take $x_i = J(e^{\rho + \overline{\omega}_i})/d$ (with the notation in no. 3).

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

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