Lie symmetries for integrable evolution equations on the lattice

In this work we show how to construct symmetries for the differential-difference equations associated with the discrete Schrodinger spectral problem. We find the whole set of symmetries which in the continuous limit go into the Lie point symmetries of the corresponding partial differential equation, i.e, the Korteweg-de Vries equation. Among these, of particular relevance, is the non-autonomous symmetry which, in the continuous limit, goes into the dilation symmetry for the corresponding equation. Unlike the continuous case, this symmetry turns out to be a master symmetry, thus belonging to the infinite-dimensional group of generalized symmetries.