Formal conserved quantities for isothermic surfaces

Isothermic surfaces in Sⁿ are characterised by the existence of a pencil  ∇^t∇∇t of flat connections. Such a surface is special of type d if there is a family p t of ∇^t-parallel sections whose dependence on the spectral parameter t is polynomial of degree d. We prove that any isothermic surface admits a family of ∇^t-parallel sections which is a formal Laurent series in t. As an application, we give conformally invariant conditions for an isothermic surface in S³ to be special.