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Journal Articles Communications in Mathematical Physics Year : 2014

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.

Dates and versions

hal-01390756 , version 1 (02-11-2016)

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