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Journal Articles Communications in Mathematical Physics Year : 2014

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.

Dates and versions

hal-00773582 , version 1 (14-01-2013)

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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, 2014. ⟨hal-00773582⟩
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