  It is well known that in some cases the spectral parameter has a group
interpretation. We discuss in detail the case of Gauss-Codazzi equations for
isothermic surfaces immersed in $E^3$. The algebra of Lie point symmetries is
4-dimensional and all these symmetries are also symmetries of the
Gaus-Weingarten equations (which can be considered as so(3)-valued
non-parametric linear problem). In order to obtain a non-removable spectral
parameter one has to consider so(4,1)-valued linear problem which has a
3-dimensional algebra of Lie point symmetries. The missing symmetry introduces
a non-removable parameter. In the second part of the paper we extend these
results on the case of isothermic immersions in arbitrary multidimensional
Euclidean spaces. In order to simplify calculations the problem was formulated
in terms of a Clifford algebra.
