TY - JOUR
T1 - On the lattice-geometry and birational group of the six-point multi-ratio equation
AU - Atkinson, James
PY - 2014/12/3
Y1 - 2014/12/3
N2 - 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 AN symmetry, and incorporates also Korteweg–de Vries-type dynamics on a sub-domain with DN 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.
AB - 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 AN symmetry, and incorporates also Korteweg–de Vries-type dynamics on a sub-domain with DN 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.
U2 - 10.1098/rspa.2014.0612
DO - 10.1098/rspa.2014.0612
M3 - Article
SN - 1364-5021
SN - 1471-2946
VL - 471
SP - 20140612
JO - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
IS - 2173
ER -