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Phys. 39, 4701 (1998).0022-248810.1063/1.1454185https://hdl.handle.net/20.500.14352/59683©2002 American Institute of Physics. This work was partially supported by Direction General de Enseñanza Superior e Investigación Científica proyecto PB98-0821Inspired by the results of Jonas, Einsenhart, Demoulin, and Bianchi on the permutability property of classical geometrical transformations of conjugate nets and its reductions-of pseudo-orthogonal, pseudo-symmetric, and pseudo-Egorov types-dressing transformations of the N-component KP hierarchy (described within the Grassmannian) are used to generate quadrilateral lattices and its corresponding reductions. As a byproduct we get the corresponding discrete dressing transformations; in particular, we characterize the vectorial fundamental discrete transformations preserving the symmetric lattice.engjournal articlehttp://dx.doi.org/10.1063/1.1454185http://scitation.aip.orgopen access51-73Circular latticesLame equationsRibaucour transformationsQuadrilateral latticesCoordinate systemsDressing methodsConjugate netsGeometric netsField-theoryDiscreteFísica-Modelos matemáticosFísica matemática