In analogy with the Liouville case we study the sl3​ Toda theory on the
lattice and define the relevant quadratic algebra and out of it we recover the
discrete W3​ algebra. We define an integrable system with respect to the
latter and establish the relation with the Toda lattice hierarchy. We compute
the the relevant continuum limits. Finally we find the quantum version of the
quadratic algebra.Comment: 12 pages, LaTe