The Toda and Painlevé Systems Associated with Semiclassical Matrix-Valued Orthogonal Polynomials of Laguerre Type

Symmetry Integrability and Geometry-Methods and Applications

article

Mattia Cafasso¹  Manuel D. de la Iglesia² 

[1] LAREMA - Université d'Angers;Instituto de Matemáticas, Universidad Nacional Autónoma de México

关键词: Painlev´e equations;    Toda lattices;    Riemann–Hilbert problems;    matrix-valued orthogonal polynomials.;   

DOI  :  10.3842/SIGMA.2018.076

来源: National Academy of Science of Ukraine

【 摘 要 】

Consider the Laguerre polynomials and deform them by the introduction in the measure of an exponential singularity at zero. In [Chen Y., Its A., J. Approx. Theory 162 (2010), 270-297] the authors proved that this deformation can be described by systems of differential/difference equations for the corresponding recursion coefficients and that these equations, ultimately, are equivalent to the Painlevé III equation and its Bäcklund/Schlesinger transformations. Here we prove that an analogue result holds for some kind of semiclassical matrix-valued orthogonal polynomials of Laguerre type.

【 授权许可】

Unknown