Okamoto's symmetry w2 of Painlevé VI is shown to act on monodromy representations as an explicit rational map made of six cluster X-mutations, equivalently a half-turn of colored hexagon triangulations.
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Okamoto's symmetry on the representation space of the sixth Painlev\'e equation
Okamoto's symmetry w2 of Painlevé VI is shown to act on monodromy representations as an explicit rational map made of six cluster X-mutations, equivalently a half-turn of colored hexagon triangulations.