A Twisted sl₂(C) Isomonodromic-Isospectral Correspondence

2025/07/09 by Alameddine, Mohamad · 1 citation
#Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.2507.06668

Abstract

The aim of this article is to generalize the isomonodromic-isospectral correspondence for meromorphic connections of rank 2 over ℙ¹ to the twisted case. More specifically, the construction of the isospectral approach is provided for the Painlevé I hierarchy, then two maps are constructed, one linking the sets of isomonodromic and isospectral Hamiltonians, another linking the set of apparent singularities to a set of isospectral coordinates.

Citations

• The Ising Model Coupled to 2D Gravity: Higher-order Painlevé Equations/The (3,4) String Equation
• Hamiltonian representation of isomonodromic deformations of twisted\n rational connections: The Painlev 'e 1 hierarchy
• Twisted wild character varieties
• Canonical structure and symmetries of the Schlesinger equations
• Geometry of 2d topological field theories
• Monodromy perserving deformation of linear ordinary differential equations with rational coefficients. II

Cited by

• The Painlevé I hierarchy: Correspondence between the isomonodromic approach and the minimal models of the KP hierarchy

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