4 – Aut | Chamber structure

$${\mathcal{R}}_{\mathbb{L}}=\{r\in \mathbb{L}\mid ⟨r,r{⟩}_{\mathbb{L}}=-2\}.$$ The collection $${\mathcal{C}}_{\mathbb{L}}=\{\bar{C}\mid C\text{co. comp. of}{\mathcal{P}}_{\mathbb{L}}\mathrm{\setminus }\bigcup _{v\in \mathcal{F}}(v{)}^{\perp },\text{Int}(\bar{C})\ne \mathrm{\varnothing }\}$$ is called a chamber structure on ${\mathcal{P}}_{\mathbb{L}}$.

A chamber is uniquely characterized by its Weyl vector

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