Non-Commutative Painlevé Equations and Hermite-Type Matrix Orthogonal Polynomials |
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Authors: | Mattia Cafasso Manuel D de la Iglesia |
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Institution: | 1. LUNAM Université, LAREMA, Université d’Angers, 2 Boulevard Lavoisier, 49100, Angers, France 2. Departamento de Análisis Matemático, Universidad de Sevilla, Apdo (P. O. BOX) 1160, 41080, Sevilla, Spain
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Abstract: | We study double integral representations of Christoffel–Darboux kernels associated with two examples of Hermite-type matrix orthogonal polynomials. We show that the Fredholm determinants connected with these kernels are related through the Its–Izergin–Korepin–Slavnov (IIKS) theory with a certain Riemann-Hilbert problem. Using this Riemann-Hilbert problem we obtain a Lax pair whose compatibility conditions lead to a non-commutative version of the Painlevé IV differential equation for each family. |
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