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

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

Research output: Contribution to journalArticle

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
Number of pages19
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume473
Issue number2207
DOIs
Publication statusPublished - 22 Nov 2017
Externally publishedYes

Keywords

  • ? function
  • ABS equation
  • Affine Weyl group
  • Discrete power function
  • Painlevé equation
  • Projective reduction

Fingerprint Dive into the research topics of 'Geometric description of a discrete power function associated with the sixth Painlevé equation'. Together they form a unique fingerprint.

  • Cite this