English

Symmetries in Connection Preserving Deformations

Exactly Solvable and Integrable Systems 2011-05-25 v3

Abstract

We wish to show that the root lattice of B\"acklund transformations of the qq-analogue of the third and fourth Painlev\'e equations, which is of type (A2+A1)(1)(A_2+ A_1)^{(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.

Cite

@article{arxiv.1101.5422,
  title  = {Symmetries in Connection Preserving Deformations},
  author = {Christopher M. Ormerod},
  journal= {arXiv preprint arXiv:1101.5422},
  year   = {2011}
}
R2 v1 2026-06-21T17:18:08.651Z