Corollary

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

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

*Let P, $P'$ be two parabolic subsets of R transformed into each other by an element of the Weyl group. If there exists a chamber C of R such that $R_+(C) \subseteq P$ and $R_+(C) \subseteq P'$ , then $P = P'$ .

This follows from Lemma 3 and Prop. 21 since the only element of $W(R)$ transforming C to C is 1, cf. no. 5, Th. 2.

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

Cited by

Nothing.

Cites

Lemma 3
Prop. 21
no. 5, Th. 2