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- W4375958623 abstract "Building upon the recent works of Bertola; Fasondini, Olver and Xu, we define a class of orthogonal polynomials on elliptic curves and establish a corresponding Riemann-Hilbert framework. We then focus on the special case, defined by a constant weight function, and use the Riemann-Hilbert problem to derive recurrence relations and differential equations for the orthogonal polynomials. We further show that the sub-class of even polynomials is associated to the elliptic form of Painlev'e VI, with the tau function given by the Hankel determinant of even moments, up to a scaling factor. The first iteration of these even polynomials relates to the special case of Painlev'e VI studied by Hitchin in relation to self-dual Einstein metrics." @default.
- W4375958623 created "2023-05-10" @default.
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- W4375958623 date "2023-05-07" @default.
- W4375958623 modified "2023-09-30" @default.
- W4375958623 title "On a class of elliptic orthogonal polynomials and their integrability" @default.
- W4375958623 doi "https://doi.org/10.48550/arxiv.2305.04404" @default.
- W4375958623 hasPublicationYear "2023" @default.
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