Fundamental system of a root system ($\Delta$)

A fundamental system $\Delta$ is a basis made of roots such that every root is a linear combination of $\Delta$ whose nonzero coefficients all have the same sign. Its members are the simple roots.

The positive system associated with a fundamental system of a root system $\Delta$ consists of the roots whose coordinates in the basis $\Delta$ are nonnegative.

The fundamental chamber is the connected componentof the complement of the reflecting hyperplanes. The Weyl group acts freely and transitively on its chambers.

For a root basis $\Delta$, the closed dominant chamber isEvery Weyl-group orbit meets it in exactly one point.