A family of Cohen-Macaulay modules over singularities of type X-t+Y-3

Let K be a field with charK not equal 3 and i, t two positive integers such that I less than or equal to i < t/2, t not equal 3i. The classification p roblem for maximal Cohen-Macaulay modules over K[[X, Y]]/(X-t + Y-3) is com plicated if t greater than or equal to 6, because there exist parameter fam ilies of non-isomorphic maximal Cohen-Macaulay modules (see [Sc], or [GK], [Yo, Ch. 9] and [DG]). Here we describe parameter families of such modules Ai, such that N/YN is a direct sum of copies of K[[X]]/(X-i), K[[X]]/(Xt-i) .