Formal conserved quantities for isothermic surfaces

Isothermic surfaces in (S^n) are characterised by the existence of a pencil (nabla ^t) of flat connections. Such a surface is special of type (d) if there is a family (p(t)) of (nabla ^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 (nabla ^t) -parallel sections which is a formal Laurent series in (t) . As an application, we give conformally invariant conditions for an isothermic surface in (S^3) to be special.