2023/06/12 by Olivier Marchal, Mohamad Alameddine, Marchal, Olivier +1
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Differential Geometry (math.DG) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.2306.07378
openalex publication_date 2023/06/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider non-twisted meromorphic connections in \mathfraksl2(ℂ) and the associated symplectic Hamiltonian structure. In particular, we provide explicit expressions of the Lax pair in the geometric gauge supplementing previous results where explicit formulas have been obtained in the oper gauge. Expressing the geometric Lax matrices requires the introduction of specific Darboux coordinates for which we provide the explicit Hamiltonian evolutions. These expressions allow to build bridges between the isomonodromic deformations and the isospectral ones. More specifically, we propose an explicit change of Darboux coordinates to obtain isospectral coordinates for which Hamiltonians match the spectral invariants. This result solves the issue left opened in \citeBertolaHarnadHurtubise2022 in the case of \mathfraksl2(ℂ).