Non-commutative Painleve' equations and Hermite-type matrix orthogonal polynomials

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 Painleve' IV differential equation for each family.
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Communications in Mathematical Physics, Springer Verlag, 2014
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https://hal.archives-ouvertes.fr/hal-00773582
Contributeur : Mattia Cafasso <>
Soumis le : lundi 14 janvier 2013 - 12:38:02
Dernière modification le : lundi 5 février 2018 - 15:00:03

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  • HAL Id : hal-00773582, version 1
  • ARXIV : 1301.2116

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Mattia Cafasso, Manuel D. De La Iglesia. Non-commutative Painleve' equations and Hermite-type matrix orthogonal polynomials. Communications in Mathematical Physics, Springer Verlag, 2014. 〈hal-00773582〉

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