Polynomial invariants of groups associated to configurations of hyperplanes over finite fields Original Research Article

Let V be an n-dimensional vector space over a field F. An arrangement of hyperplanes A = {H1,…, Hk} in V is said to be in general position if whenever j Σ N lies between 1 and min(n,k) the dimension of the intersection of any j hyperplanes in A has codimension j. In this note we examine several subgroups of GL(n, F) associated with such an arrangement and the corresponding rings of polynomial invariants.