Six-vertex model and non-linear differential equations II. Continuous symmetries

This paper is a continuation of our previous work Six-vertex model and non-linear differential equations I. Spectral problem in which we have put forward a method for studying the spectrum of the six-vertex model based on non-linear differential equations. Here we intend to elaborate on that approach and also discuss properties of the spectrum unveiled by the aforementioned differential formulation of the transfer matrixs eigenvalue problem. In particular, we intend to demonstrate how this differential approach allows one to study continuous symmetries of the transfer matrixs spectrum through the Lie groups method.