Quadrics defined by skew-symmetric matrices

In this paper we propose a model for computing a minimal free resolution for ideals of the form I1(XnYn), where Xn is an n n skew-symmetric matrix with indeterminate entries xij and Yn is a generic column matrix with indeterminate entries yj. We verify that the model works for n = 3 and n = 4 and pose some statements as conjectures. Answering the conjectures in a rmative would enable us to computea minimal free resolution for general n.