Orbifold equivalent potentials

To a graded finite-rank matrix factorisation of the difference of two homogeneous potentials one can assign two numerical invariants, the left and right quantum dimensions. The existence of such a matrix factorisation with non-zero quantum dimensions defines an equivalence relation between potentials, giving rise to non-obvious equivalences of categories.Restricted to ADE singularities, the resulting equivalence classes of potentials are those of type {Ad−1}{Ad−1} for d   odd, {Ad−1,Dd/2+1}{Ad−1,Dd/2+1} for d   even but not in {12,18,30}{12,18,30}, and {A11,D7,E6}{A11,D7,E6}, {A17,D10,E7}{A17,D10,E7} and {A29,D16,E8}{A29,D16,E8}. This is the result expected from two-dimensional rational conformal field theory, and it directly leads to new descriptions of and relations between the associated (derived) categories of matrix factorisations and Dynkin quiver representations.