  After having established elementary results on the relationship between a
finite complex (pseudo-)reflection group W < GL(V) and its reflection
arrangement A, we prove that the action of W on A is canonically related with
other natural representations of W, through a `periodic' family of
representations of its braid group. We also prove that, when W is irreducible,
then the squares of defining linear forms for A span the quadratic forms on V,
which imply |A| >= n(n+1)/2 for n = dim V, and relate the W-equivariance of the
corresponding map with the period of our family.

Representation Theory;Group Theory