Symmetries in Connection Preserving Deformations

Symmetry Integrability and Geometry-Methods and Applications

article

Christopher M. Ormerod¹ 

[1] La Trobe University, Department of Mathematics and Statistics

关键词: q-Painlev´e;    Lax pairs;    q-Schlesinger transformations;    connection;    isomonodromy;   

DOI  :  10.3842/SIGMA.2011.049

来源: National Academy of Science of Ukraine

【 摘 要 】

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 ( 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.

【 授权许可】

Unknown