Symmetries in Connection Preserving Deformations

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 $(A_2+A_1{)}^{(1)}$, 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.

References in corpus (9)

• Algebraic entropy
• Affine Weyl groups, discrete dynamical systems and Painleve equations
• A study on the fourth q-Painlevé equation
• Lax forms of the $q$-Painlevé equations
• On a q-difference Painlevé III equation: I. Derivation, symmetry and Riccati type solutions
• Algebraic construction of the Stokes sheaf for irregular linear q-difference equations
• Galois theory of q-difference equations
• The Lattice Structure of Connection Preserving Deformations for q-Painlevé Equations I
• A study of the associated linear problem for $q$-${\mathrm{P}}_{\mathrm{V}}$

Cited by in corpus (1)

• Commutation Relations and Discrete Garnier Systems