On the lattice-geometry and birational group of the six-point multi-ratio equation
arXiv:1407.5468 · doi:10.1098/rspa.2014.0612
Abstract
The inherent self-consistency properties of the six-point multi-ratio equation allow it to be considered on a domain associated with a T-shaped Coxeter-Dynkin diagram. This extends the KP lattice, which has A_N symmetry, and incorporates also KdV-type dynamics on a sub-domain with D_N symmetry, and Painleve dynamics on a sub-domain with affine-E8 symmetry. More generally, it can be seen as a distinguished representation of Coble's Cremona group associated with invariants of point sets in projective space.
arXiv comment20 pages, 3 figures
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