Remark 1

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

Lie Groups and Lie Algebras, chapter V, § 3. Groups of displacements generated by reflections

Identify $E$ with $E_0 \times E_1 \times \cdots \times E_s$ and $W$ with $W_1 \times \cdots \times W_s$ as in no. 8. By Prop. 6, the chamber $C$ is then identified with

E_0 \times C_1 \times \cdots \times C_s,

where $C_p$ is a chamber in $E_p$ with respect to the set of hyperplanes $\mathscr{H}_p$ . By Props. 7 and 8, each of the chambers $C_1, \ldots, C_s$ is an open simplicial cone or an open simplex.

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

Cited by

Nothing.

Cites

Prop. 6