Fundamental Chamber of a Finite Reflection Group Suppose that a **finite reflection group G** is generated by the reflections: $r_1, r_2, \dots r_n$. What is **precisely** meant by the **Fundamental Chamber of G?** Does this definiton depend on the choice of generators for G? That is, if G is also generated by the reflections $s_1, s_2, \dots, s_m$, then is the notion of Fundamental Chamber different now?

I try to give you a panoramic view of the situation:

We have a group $G$ generated by the reflections $r_1 , \dots, r_n$.

In the classical contest this group is realized as a group of endomorphism of an euclidean space of finite dimension $E$ with inner product $ \langle \; , \, \rangle $, where the reflections are precisely the reflections of the space that leave fixed an hyperplane.

So to every reflection $r_i$ is associatend an hyperplane $H_i$.

A **Chamber** for (the action of) $G$ is a connected component of $V \setminus \cup_i H_i$.

Now, let suppose $H_i$ generated by a vector $h_i$.

The **Foundamental Chamber** for (the action of) $G$ is the only chamber $C $ such that there exist a vector $v \in C$ with the property $\langle v, h_i \rangle \geq 0 $ for every $h_i$.

Now, If I well remember this construction depends only by the group and not by the generators, but i think you can find every informations you need in some specialized book like Humphreys's one.