On some Hall polynomials over a quiver of type ˜D₄

Let k be an arbitrary field and Q a tame quiver of type ˜D4. Consider the path algebra kQ and the category of finite dimensional right modules mod-kQ. We determine the Hall polynomials F_xy^z associated to indecomposable modules of defect ∂z =−2, ∂x = ∂y =−1 or dually ∂z = 2, ∂x = ∂y = 1.