Toda lattice field theories, discrete W algebras, Toda lattice hierarchies and quantum groups

Abstract

In analogy with the Liouville case we study the $s{l}_3$ Toda theory on the 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 the relevant continuum limits. Finally we find the quantum version of the quadratic algebra.

12 pages, LaTeX

References in corpus (7)

• Lattice Wess-Zumino-Witten Model and Quantum Groups
• Lattice analogues of W-algebras and Classical Integrable Equations
• Multi-field representations of KP hierarchies and multi-matrix models
• Lattice Analogue of W-infinity Algebra and Discrete KP-Hierarchy
• Geometry of Higgs and Toda Fields on Riemann Surfaces
• Integrable Discrete Linear Systems and One-Matrix Model
• Quantum sl_n Toda field theories

Cited by in corpus (2)

• T-systems and Y-systems in integrable systems
• The matrix realization of affine Jacobi varieties and the extended Lotka-Volterra lattice