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.

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Submitted on : Wednesday, November 2, 2016 - 2:01:47 PM
Last modification on : Wednesday, December 19, 2018 - 2:08:04 PM

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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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