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arXiv · 1006.3380

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

Adam Doliwa
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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.

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Adam Doliwa. 2010-06-17. The affine Weyl group symmetry of Desargues maps and of the non-commutative Hirota-Miwa system. https://doi.org/10.1016/j.physleta.2011.01.050

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