Service interruption on Monday 11 July from 12:30 to 13:00: all the sites of the CCSD (HAL, Epiciences, SciencesConf, AureHAL) will be inaccessible (network hardware connection).
Skip to Main content Skip to Navigation
Journal articles

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.

Document type :
Journal articles
Complete list of metadata
Contributor : Okina Univ Angers Connect in order to contact the contributor
Submitted on : Wednesday, November 2, 2016 - 2:01:47 PM
Last modification on : Wednesday, October 20, 2021 - 3:18:54 AM

Links full text




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⟩



Record views