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

2022/12/30 by Li, Shi-Hao, Shi, Ying, Yu, Guo-Fu +1 · 3 citations
#Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2212.14512

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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• Quasi-Pfaffians and applications
• Nonisospectral deformations of noncommutative Laurent biorthogonal polynomials and matrix discrete Painlevé-type equations
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