  Let k be a field of characteristic zero. We consider graded subalgebras A of
k[x_1,...,x_m]/(x_1^2,...,x_m^2) generated by d linearly independant linear
forms. Representations of matroids over k provide a natural description of the
structure of these algebras. In return, the numerical properties of the Hilbert
function of A yield some information about the Tutte polynomial of the
corresponding matroid. Isomorphism classes of these algebras correspond to
equivalence classes of hyperplane arrangements under the action of the general
linear group.
