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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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https://hal.archives-ouvertes.fr/hal-00773582
Contributor : Mattia Cafasso Connect in order to contact the contributor
Submitted on : Monday, January 14, 2013 - 12:38:02 PM
Last modification on : Wednesday, October 20, 2021 - 3:18:52 AM

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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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