Lattice analogues of W-algebras and Classical Integrable Equations

Abstract

We propose a regular way to construct lattice versions of $W$-algebras, both for quantum and classical cases. In the classical case we write the algebra explicitly and derive the lattice analogue of Boussinesq equation from the Hamiltonian equations of motion. Connection between the lattice Faddeev-Takhtadjan-Volkov algebra [1] and q-deformed Virasoro is also discussed.

LaTeX, ILG-TMP-93-01, (the problems caused by mailer are fixed)

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• Systematic method of generating new integrable systems via inverse Miura maps
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• Darboux Covariant Equations of von Neumann Type and their Generalizations
• Toda lattice field theories, discrete W algebras, Toda lattice hierarchies and quantum groups
• Extension of the discrete KP hierarchy
• Baxter Equation for Quantum Discrete Boussinesq Equation
• On some class of reductions for Itoh-Narita-Bogoyavlenskii lattice
• On some classes of discrete polynomials and ordinary difference equations
• Lattice Virasoro from Lattice Kac-Moody
• Reductions of integrable lattices
• Bogoyavlensky lattices and generalized Catalan numbers