Let ∆ be a finite set of nonzero linear forms in several variables with coefficients in a field K of characteristic zero. Consider the K-algebra C(∆) of rational functions generated by {1/α | α ∈ ∆}. Then the ring ∂(V ) of differential operators with constant coefficients naturally acts on C(∆). We study the graded ∂(V )-module structure of C(∆). We especially find standard systems of minimal generators and a combinatorial formula for the Poincaré series of C(∆). Our proofs are based on a… CONTINUE READING