The affine Weyl group symmetry of Desargues maps and of the non-commutative Hirota-Miwa system
arXiv:1006.3380 · doi:10.1016/j.physleta.2011.01.050
Abstract
We study recently introduced Desargues maps, which provide simple geometric interpretation of the non-commutative Hirota--Miwa system. We characterize them as maps of the A-type root lattice into a projective space such that images of vertices of any basic regular N-simplex are collinear. Such a characterization is manifestly invariant with respect to the corresponding affine Weyl group action, which leads to related symmetries of the Hirota--Miwa system.
arXiv comment10 pages, 1 figure
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