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arXiv · 2504.18891

Cauchy-Jacobi orthogonal polynomials and the discrete CKP equation

Shi-Hao Li·Satoshi Tsujimoto·Ryoto Watanabe·Guo-Fu Yu
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Abstract

This paper intends to construct discrete spectral transformations for Cauchy-Jacobi orthogonal polynomials, and find its corresponding discrete integrable systems. It turns out that the normalization factor of Cauchy-Jacobi orthogonal polynomials acts as the $\tau$-function of the discrete CKP equation, which has applications in Yang-Baxter equation, integrable geometry, cluster algebra, and so on.

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Shi-Hao Li, Satoshi Tsujimoto, Ryoto Watanabe, Guo-Fu Yu. 2025-04-26. Cauchy-Jacobi orthogonal polynomials and the discrete CKP equation. https://arxiv.org/abs/2504.18891

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