Contents
Part I Special Session in Honour of Decio Levi: Integrability:
Continuous and Discrete, Classical & Quantum
Spin Chains of Haldane–Shastry Type: A Bird’s Eye View . . . . . . . . . . . . . . . . .
3
Federico Finkel, Artemio González-López, and Miguel A. Rodríguez
Features of Discrete Integrability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
Claude M. Viallet
Darboux-Bäcklund Transformations for Spin-Valued Linear Problems. . . . 37
Jan L. Cie´ sli´ nski
Painlevé IV Transcendents Generated from the Complex Oscillator . . . . . . 47
David J. Fernández
The Veronese Sequence of Analytic Solutions of the CP 2s Sigma
Model Equations Described via Krawtchouk Polynomials . . . . . . . . . . . . . . . . . . 57
Nicolas Crampé and Alfred Michel Grundland
A Novel Integrable Fourth-Order Difference Equation Admitting
Three Invariants. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
Giorgio Gubbiotti
Weighted Hurwitz Numbers, τ-Functions, and Matrix Integrals. . . . . . . . . . . 77
J. Harnad
Constant Curvature Holomorphic Solutions of the Supersymmetric
G(2, 4) Sigma Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
Véronique Hussin, Marie Lafrance, and ˙
Ismet Yurdu¸ sen
How to Deal with Nonlocality and Pseudodifferential Operators.
An Example: The Salpeter Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
A. Lattanzi
xiii
Part I Special Session in Honour of Decio Levi: Integrability:
Continuous and Discrete, Classical & Quantum
Spin Chains of Haldane–Shastry Type: A Bird’s Eye View . . . . . . . . . . . . . . . . .
3
Federico Finkel, Artemio González-López, and Miguel A. Rodríguez
Features of Discrete Integrability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
Claude M. Viallet
Darboux-Bäcklund Transformations for Spin-Valued Linear Problems. . . . 37
Jan L. Cie´ sli´ nski
Painlevé IV Transcendents Generated from the Complex Oscillator . . . . . . 47
David J. Fernández
The Veronese Sequence of Analytic Solutions of the CP 2s Sigma
Model Equations Described via Krawtchouk Polynomials . . . . . . . . . . . . . . . . . . 57
Nicolas Crampé and Alfred Michel Grundland
A Novel Integrable Fourth-Order Difference Equation Admitting
Three Invariants. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
Giorgio Gubbiotti
Weighted Hurwitz Numbers, τ-Functions, and Matrix Integrals. . . . . . . . . . . 77
J. Harnad
Constant Curvature Holomorphic Solutions of the Supersymmetric
G(2, 4) Sigma Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
Véronique Hussin, Marie Lafrance, and ˙
Ismet Yurdu¸ sen
How to Deal with Nonlocality and Pseudodifferential Operators.
An Example: The Salpeter Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
A. Lattanzi
xiii