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Non-commutative Painlevé equations and Hermite-type matrix orthogonal polynomials

 

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Opened Access Non-commutative Painlevé equations and Hermite-type matrix orthogonal polynomials
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Author: Cafasso, Mattia
Domínguez de la Iglesia, Manuel
Department: Universidad de Sevilla. Departamento de Análisis Matemático
Date: 2014-03
Published in: Communications in Mathematical Physics, 326 (2), 559-583.
Document type: Article
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.
Cite: 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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URI: http://hdl.handle.net/11441/42397

DOI: http://dx.doi.org/10.1007/s00220-013-1853-4

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