Geometric Analysis of Reductions from Schlesinger Transformations to Difference Painlevé Equations

2014/08/17 by Anton Dzhamay, Dzhamay, Anton, Tomoyuki Takenawa +1
Chemistry · #14E07 #34M55 #34M56 #Algebraic Geometry (math.AG) #Axial and Atropisomeric Chirality Synthesis #Classical Analysis and ODEs (math.CA) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Molecular spectroscopy and chirality

paper · pdf · doi:10.48550/arxiv.1408.3778

openalex publication_date 2014/08/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present two examples of reductions from the evolution equations describing discrete Schlesinger transformations of Fuchsian systems to difference Painlevé equations: difference Painlevé equation d-P(A₂^(1)*) with the symmetry group E⁽¹⁾₆ and difference Painlevé equation d-P(A₁^(1)*) with the symmetry group E⁽¹⁾₇. In both cases we describe in detail how to compute their Okamoto space of the initial conditions and emphasize the role played by geometry in helping us to understand the structure of the reduction, a choice of a good coordinate system describing the equation, and how to compare it with other instances of equations of the same type.

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