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 Kadomtsev–Petviashvili lattice, which has A N symmetry, and incorporates also Korteweg–de Vries-type dynamics on a sub-domain with D N symmetry, and Painlevé dynamics on a sub-domain with E ~ 8 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.

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