  This paper is devoted to a study of the connections between three different
analytic descriptions for the immersion functions of 2D-surfaces corresponding
to the following three types of symmetries: gauge symmetries of the linear
spectral problem, conformal transformations in the spectral parameter and
generalized symmetries of the associated integrable system. After a brief
exposition of the theory of soliton surfaces and of the main tool used to study
classical and generalized Lie symmetries, we derive the necessary and
sufficient conditions under which the immersion formulas associated with these
symmetries are linked by gauge transformations. We illustrate the theoretical
results by examples involving the sigma model.
