The affine Weyl group symmetry of Desargues maps and of the non-commutative Hirota-Miwa system

Details The affine Weyl group symmetry of Desargues maps and of the non-commutative Hirota-Miwa system The affine Weyl group symmetry of Desargues maps and of the non-commutative Hirota-Miwa system

2010-06-17

arxiv.org/abs/1006.3380v1

Phys. Lett. A 375 (2011) 1219-1224

Nonlinear Sciences

Exactly Solvable and Integrable Systems

10 pages, 1 figure

Scientific paper

10.1016/j.physleta.2011.01.050

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.

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