TY - JOUR

T1 - Geometric description of a discrete power function associated with the sixth Painlevé equation

AU - Joshi, Nalini

AU - Kajiwara, Kenji

AU - Masuda, Tetsu

AU - Nakazono, Nobutaka

AU - Shi, Yang

N1 - Publisher Copyright:
© 2017 The Author(s) Published by the Royal Society. All rights reserved.

PY - 2017/11/1

Y1 - 2017/11/1

N2 - In this paper, we consider the discrete power function associated with the sixth Painlevé equation. This function is a special solution of the so-called cross-ratio equation with a similarity constraint. We show in this paper that this system is embedded in a cubic lattice with W (3A(1)1 ) symmetry. By constructing the action of W (3A(1)1 ) as a subgroup of W (D(1)4 ), i.e. the symmetry group of PVI, we show how to relate W (D(1)4 ) to the symmetry group of the lattice. Moreover, by using translations in W (3A(1)1 ), we explain the odd–even structure appearing in previously known explicit formulae in terms of the t function.

AB - In this paper, we consider the discrete power function associated with the sixth Painlevé equation. This function is a special solution of the so-called cross-ratio equation with a similarity constraint. We show in this paper that this system is embedded in a cubic lattice with W (3A(1)1 ) symmetry. By constructing the action of W (3A(1)1 ) as a subgroup of W (D(1)4 ), i.e. the symmetry group of PVI, we show how to relate W (D(1)4 ) to the symmetry group of the lattice. Moreover, by using translations in W (3A(1)1 ), we explain the odd–even structure appearing in previously known explicit formulae in terms of the t function.

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U2 - 10.1098/rspa.2017.0312

DO - 10.1098/rspa.2017.0312

M3 - Article

AN - SCOPUS:85037720560

SN - 1364-5021

VL - 473

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 - 2207

M1 - 20170312

ER -