The linear space of Betti diagrams of multigraded artinian modules

We study the linear space generated by the multigraded Betti diagrams of Z^n-graded artinian modules of codimension n whose resolutions become pure of a given type when taking total degrees. We show that the multigraded Betti diagram of the equivariant resolution constructed by D.Eisenbud, J.Weyman, and the author, and all its twists, form a basis for this linear space.