Schur partial derivative operators

A lattice diagram is a finite list L = ( ( p 1 , q 1 ) , … , ( p n , q n ) ) of lattice cells. The corresponding lattice diagram determinant is Δ L ( X ; Y ) = det ‖ x i p j y i q j ‖ . The space M L is the space spanned by all partial derivatives of Δ L ( X ; Y ) . We describe here how a Schur function partial derivative operator acts on lattice diagrams with distinct cells in the positive quadrant.