Discrete Levy Transformations and Casorati Determinant Solutions of Quadrilateral Lattices

Abstract

Sequences of discrete Levy and adjoint Levy transformations for the multidimensional quadrilateral lattices are studied. After a suitable number of iterations we show how all the relevant geometrical features of the transformed quadrilateral lattice can be expressed in terms of multi-Casorati determinants. As an example we dress the Cartesian lattice.

12 pages, LaTeX2e using AMSLaTeX package

References in corpus (2)

• Multidimensional Quadrilateral Lattices are Integrable
• Sequences of Levy Transformations and Multi-Wroński Determinant Solutions of the Darboux System

Cited by in corpus (6)

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• Bäcklund transformations as integrable discretization. The geometric approach