On associated graded modules having a pure resolution

Let $A=K[[X_1,\cdots ,X_n]]$ and let $\mathfrak{m}=(X_1,\cdots ,X_n)$. Let $M$ be a Cohen-Macaulay $A$-module of codimension $p$. In this paper we give a necessary and sufficient condition for the associated graded module $G_{\mathfrak{m}}(M)$ to have a pure resolution over the polynomial ring $G_{\mathfrak{m}}(A)\cong K[X_1,\cdots ,X_n]$.