arrangementsreflecting
Arrangements reflecting, more commonly known as reflection arrangements or Coxeter arrangements, are a class of hyperplane arrangements arising from finite reflection groups. Given a real vector space V of dimension n and a finite Coxeter group W acting on V by orthogonal transformations, the reflection arrangement A(W) is the collection of all reflecting hyperplanes corresponding to the reflections in W. Equivalently, A(W) consists of the hyperplanes fixed by reflections in W, and all hyperplanes pass through the origin, making A(W) a central arrangement.
The defining data of a reflection arrangement is the underlying root system or the Coxeter system associated
Key invariants include the characteristic polynomial χ_A(t) of the arrangement, which for a finite Coxeter group
Prominent examples include type A_n (the braid arrangement, hyperplanes x_i = x_j), type B_n/C_n, type D_n, and