Schur partial derivative operators

A lattice diagram is a finite list L=((p1,q1),…,(pn,qn)) of lattice cells. The corresponding lattice diagram determinant is ΔL(X;Y)=det‖xipjyiqj‖. The space ML is the space spanned by all partial derivatives of ΔL(X;Y). We describe here how a Schur function partial derivative operator acts on lattice diagrams with distinct cells in the positive quadrant.