The squared eigenfunction symmetries of the discrete KP and modified discrete KP hierarchies under the Miura transformations

In this paper, we investigate the squared eigenfunction symmetries under the Miura and reverse-Miura transformations, between the discrete KP and modified discrete KP hierarchies, in unconstrained and constrained cases. What is more, the squared eigen-function symmetries for the constrained discrete KP and constrained modified discrete KP hierarchies are constructed by imposing the additional conditions on the generating eigenfunctions of the corresponding symmetries.