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 language | English |
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Article number | 20170312 |
Journal | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences |
Volume | 473 |
Issue number | 2207 |
DOIs | |
Publication status | Published - Nov 1 2017 |
All Science Journal Classification (ASJC) codes
- Mathematics(all)
- Engineering(all)
- Physics and Astronomy(all)