Non-Commutative Painlevé 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 Painlevé IV differential equation for each family.

Type de document :
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Communications in Mathematical Physics, Springer Verlag, 2014, 326 (2), pp.559-583. 〈10.1007/s00220-013-1853-4〉
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https://hal.archives-ouvertes.fr/hal-01390756
Contributeur : Okina Université d'Angers <>
Soumis le : mercredi 2 novembre 2016 - 14:01:47
Dernière modification le : lundi 5 février 2018 - 15:00:03

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Mattia Cafasso, Manuel De La Iglesia. Non-Commutative Painlevé Equations and Hermite-Type Matrix Orthogonal Polynomials. Communications in Mathematical Physics, Springer Verlag, 2014, 326 (2), pp.559-583. 〈10.1007/s00220-013-1853-4〉. 〈hal-01390756〉

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