Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 7 (2011), 049, 13 pages      arXiv:1101.5422      https://doi.org/10.3842/SIGMA.2011.049
Contribution to the Proceedings of the Conference “Symmetries and Integrability of Difference Equations (SIDE-9)”

Symmetries in Connection Preserving Deformations

Christopher M. Ormerod
La Trobe University, Department of Mathematics and Statistics, Bundoora VIC 3086, Australia

Received January 31, 2011, in final form May 18, 2011; Published online May 24, 2011

Abstract
We wish to show that the root lattice of Bäcklund transformations of the q-analogue of the third and fourth Painlevé equations, which is of type (A2+A1)(1), may be expressed as a quotient of the lattice of connection preserving deformations. Furthermore, we will show various directions in the lattice of connection preserving deformations present equivalent evolution equations under suitable transformations. These transformations correspond to the Dynkin diagram automorphisms.

Key words: q-Painlevé; Lax pairs; q-Schlesinger transformations; connection; isomonodromy.

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