Irreducible circuits and Coxeter arrangements

We introduce the concept of irreducible circuits. In a vector arrangement Φ, these are configurations consisting of one vector α ∈ Φ in the positive linear span of an independent set Δ ⊂ Φ such that no proper subset of Δ has any member of Φ − Δ in its positive linear span. We show that the oriented matroid of any centrally symmetric vector arrangement is constructively determined by its irreducible circuits, and classify the irreducible circuits in root systems.