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arXiv · 2305.17962

Matrix-valued $\theta$-deformed bi-orthogonal polynomials, Non-commutative Toda theory and B\"acklund transformation

Claire Gilson·Shi-Hao Li·Ying Shi
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Abstract

This paper is devoted to revealing the relationship between matrix-valued $\theta$-deformed bi-orthogonal polynomials and non-commutative Toda-type hierarchies. In this procedure, Wronski quasi-determinants are widely used and play the role of non-commutative $\tau$-functions. At the same time, B\"acklund transformations are realized by using a moment modification method and non-commutative $\theta$-deformed Volterra hierarchies are obtained, which contain the known examples of the Itoh-Narita-Bogoyavlensky lattices and the fractional Volterra hierarchy.

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Claire Gilson, Shi-Hao Li, Ying Shi. 2023-05-29. Matrix-valued $\theta$-deformed bi-orthogonal polynomials, Non-commutative Toda theory and B\"acklund transformation. https://arxiv.org/abs/2305.17962

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