L. Bonora et al., TODA LATTICE FIELD-THEORIES, DISCRETE W-ALGEBRAS, TODA LATTICE HIERARCHIES AND QUANTUM GROUPS, Physics letters. Section B, 387(4), 1996, pp. 759-768
In analogy with the Liouville case we study the sl(3) Toda theory on t
he lattice and define the relevant quadratic algebra and out of it we
recover the discrete W-3 algebra. We define an integrable system with
respect to the latter and establish the relation with the Toda lattice
hierarchy. We compute the relevant continuum limits. Finally we find
the quantum version of the quadratic algebra.