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arXiv · 2507.06668

A Twisted sl_2(C) Isomonodromic-Isospectral Correspondence

Mohamad Alameddine
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Abstract

The aim of this article is to generalize the isomonodromic-isospectral correspondence for meromorphic connections of rank $2$ over $\mathbb{P}^1$ to the twisted case. More specifically, the construction of the isospectral approach is provided for the Painlev\'{e} 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.

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Mohamad Alameddine. 2025-07-09. A Twisted sl_2(C) Isomonodromic-Isospectral Correspondence. https://arxiv.org/abs/2507.06668

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