The elliptic-mutation conjecture for elliptic isomonodromic flows

Consider elliptic cluster algebras associated with elliptic generalizations of cluster mutations, and elliptic isomonodromic deformation flows. Elliptic-mutation conjecture. Elliptic isomonodromic deformation flows can be obtained as combinations of elliptic mutations in the corresponding elliptic cluster algebras. This extends the proposed elliptic cluster description from monodromy-manifold automorphisms to the isomonodromic flows themselves; the supplied text gives no resolution.

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Primary source

Pavlo Gavrylenko, “Riemann-Hilbert problems, Fredholm determinants, explicit combinatorial expansions, and connection formulas for the general q-Painlevé III_3 tau functions”, arXiv:2501.01419 (2025).

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