Corollary 2
Tag 0ARK, permanent. Cite it as [Bourbaki, Tag 0ARK].
Lie Groups and Lie Algebras, chapter V, § 4. The geometric representation of a Coxeter group
The representations σ and σ* are injective.
Indeed, if σ*(w) = 1, then w(C) = C, so w = 1 by the theorem. The injectivity of σ follows from that of σ*.
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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