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, Wei Fu School of Mathematical Sciences, Key Laboratory of Mathematics and Engineering Applications (Ministry of Education) & Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice, East China Normal University , Shanghai 200241, People’s Republic of China Search for other works by this author on: Oxford Academic Shi-Hao Li School of Mathematics, Sichuan University , Chengdu 610064, People’s Republic of China Correspondence to be sent to: e-mail: lishihao@lsec.cc.ac.cn Search for other works by this author on: Oxford Academic
International Mathematics Research Notices, Volume 2024, Issue 10, May 2024, Pages 8695–8715, https://doi.org/10.1093/imrn/rnad305
Published:
24 January 2024
Article history
Received:
21 July 2023
Revision received:
21 July 2023
Accepted:
28 November 2023
Published:
24 January 2024
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Wei Fu, Shi-Hao Li, Skew-Orthogonal Polynomials and Pfaff Lattice Hierarchy Associated With an Elliptic Curve, International Mathematics Research Notices, Volume 2024, Issue 10, May 2024, Pages 8695–8715, https://doi.org/10.1093/imrn/rnad305
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Abstract
Starting with a skew-symmetric inner product over an elliptic curve, we propose the concept of elliptic skew-orthogonal polynomials. Inspired by the Landau–Lifsh*tz hierarchy and its corresponding time evolutions, we obtain the recurrence relation and the |$\tau $|-function representation for such a novel class of skew-orthogonal polynomials. Furthermore, a bilinear integral identity is derived through the so-called Cauchy–Stieljes transformation, from which we successfully establish the connection between the elliptic skew-orthogonal polynomials and an elliptic extension of the Pfaff lattice hierarchy.
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