Nonisospectral Deformations of Noncommutative Laurent Biorthogonal Polynomials and Matrix Discrete Painlevé‐Type Equations

ABSTRACT In this paper, we establish a connection between noncommutative Laurent biorthogonal polynomials (bi‐OPs) and matrix discrete Painlevé (dP) equations. We first apply nonisospectral deformations to noncommutative Laurent bi‐OPs to obtain the noncommutative nonisospectral mixed relativistic Toda lattice and its Lax pair. Then, we perform a stationary reduction on this Lax pair to obtain a matrix dP‐type equation. The validity of this reduction is demonstrated through a specific choice of weight function and the application of quasideterminant properties. In the scalar case, our matrix dP equation reduces to the known alternate dP II equation.