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Matrix-valued Cauchy bi-orthogonal polynomials and a novel noncommutative integrable lattice (2212.14512v1)
Published 30 Dec 2022 in math-ph, math.MP, and nlin.SI
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.