An Elliptic Garnier System from Interpolation

Abstract

Considering a certain interpolation problem, we derive a series of elliptic difference isomonodromic systems together with their Lax forms. These systems give a multivariate extension of the elliptic Painlevé equation.

References in corpus (8)

• Essays on the theory of elliptic hypergeometric functions
• A Lax Formalism for the Elliptic Difference Painlevé Equation
• An Isomonodromy Interpretation of the Hypergeometric Solution of the Elliptic Painlevé Equation (and Generalizations)
• Commutation Relations and Discrete Garnier Systems
• Padé interpolation for elliptic Painlevé equation
• Study of $q$-Garnier system by Padé method
• An elliptic Garnier system
• The noncommutative geometry of elliptic difference equations

Cited by in corpus (6)

• On determinant representation and integrability of Nekrasov functions
• Variations of $q$-Garnier system
• The Elliptic Painlevé Lax Equation vs. van Diejen's 8-Coupling Elliptic Hamiltonian
• Quantum Representation of Affine Weyl Groups and Associated Quantum Curves
• A Variation of the $q$-Painlevé System with Affine Weyl Group Symmetry of Type $E_7^{(1)}$
• Connection Problem for an Extension of $q$-Hypergeometric Systems