ON DISCRETE SYSMMETRIES OF THE MULTI-BOSON KP HIERARCHIES

We show that the multi-boson KP hierarchies possess a class of discret e symmetries linking them to discrete Toda systems. These discrete sym metries are generated by the similarity transformation of the correspo nding Lax operator. This establishes a canonical nature of the discret e transformations. The spectral equation, which defines both the latti ce system and the corresponding Lax operator, plays a key role in dete rmining pertinent symmetry structure. We also introduce the concept of the square root lattice leading to a family of new pseudo-differentia l operators with covariance under additional Backlund transformations.