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

Nalini Joshi, Kenji Kajiwara, Tetsu Masuda, Nobutaka Nakazono, Yang Shi

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1 Citation (Scopus)

Abstract

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.

Original languageEnglish
Article number20170312
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume473
Issue number2207
DOIs
Publication statusPublished - Nov 1 2017

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Engineering(all)
  • Physics and Astronomy(all)

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