  Let $A$ be a $d\times n$ integer matrix whose column vectors generate the
lattice $\Z^d$, and let $D(R_A)$ be the ring of differential operators on the
affine toric variety defined by $A$.
  We show that the classification of $A$-hypergeometric systems and that of
$\Z^d$-graded simple $D(R_A)$-modules (up to shift) are the same. We then show
that the set of $\Z^d$-homogeneous primitive ideals of $D(R_A)$ is finite.
Furthermore, we give conditions for the algebra $D(R_A)$ being simple.
