Article
Non-commutative Painlevé equations and Hermite-type matrix orthogonal polynomials
Author/s | Cafasso, Mattia
Domínguez de la Iglesia, Manuel |
Department | Universidad de Sevilla. Departamento de Análisis Matemático |
Publication Date | 2014-03 |
Deposit Date | 2016-06-16 |
Published in |
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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 ... 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. |
Project ID. | info:eu-repo/grantAgreement/MINECO/MTM2012-36732-C03-03
FQM-262 FQM-4643 FQM-7276 |
Citation | Cafasso, M. y Domínguez de la Iglesia, M. (2014). Non-commutative Painlevé equations and Hermite-type matrix orthogonal polynomials. Communications in Mathematical Physics, 326 (2), 559-583. |
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