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arXiv · 2212.14512

Matrix-valued Cauchy bi-orthogonal polynomials and a novel noncommutative integrable lattice

Shi-Hao Li·Ying Shi·Guo-Fu Yu·Jun-Xiao Zhao
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Abstract

Matrix-valued Cauchy bi-orthogonal polynomials were proposed in this paper, together with its quasideterminant expression. It is shown that the coefficients in four-term recurrence relation for matrix-valued Cauchy bi-orthogonal polynomials should satisfy a novel noncommutative integrable system, whose Lax pair is given by fractional differential operators with non-abelian variables.

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Shi-Hao Li, Ying Shi, Guo-Fu Yu, Jun-Xiao Zhao. 2022-12-30. Matrix-valued Cauchy bi-orthogonal polynomials and a novel noncommutative integrable lattice. https://arxiv.org/abs/2212.14512

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