Group Analysis of Differential Equations and Integrable Systems − 2018

Nobutaka Nakazono (Aoyama Gakuin University, Tokyo, Japan)

Affine Weyl group symmetry of the discrete power function

In this talk, we show that the discrete power function associated with circle patterns of Schramm type can be obtained from a space-filling cubic lattice, each cube has CAC property, and its affine Weyl group symmetry. Moreover, we show that this cubic lattice and its symmetry are derived form the affine Weyl group symmetry of the sixth Painlevé equation.

This work has been done in collaboration with Profs Nalini Joshi, Kenji Kajiwara, Tetsu Masuda and Dr Yang Shi.