The lattice Gel'fand-Dikii hierarchy

Using the direct linearization method the authors construct lattice versions of the hierarchy of Gel'fand-Dikii equations, the first members being the lattice KdV equation and the lattice Boussinesq equation. The (local) initial value problem on the lattice of this family of equations is formulated, giving rise to integrable multi-dimensional mappings. The involutivity of the invariants of these mappings is established on the basis of a novel classical tau -matrix structure.