Nonisospectral deformations of noncommutative orthogonal polynomials and matrix discrete Painlevé-type equations

In this paper, nonisospectral deformations of noncommutative orthogonal polynomials are investigated. On one hand, nonisospectral deformations are carried out on noncommutative orthogonal polynomials, specifically matrix orthogonal polynomials, leading to noncommutative nonisospectral Toda and Lotka–Volterra lattices. On the other hand, stationary reduction is applied to the obtained noncommutative nonisospectral integrable lattices and their Lax pairs, resulting in matrix discrete Painlevé-type equations and their Lax pairs, respectively. Furthermore, the quasideterminant solutions are provided for the matrix discrete Painlevé-type equations which guarantees the validity of the stationary reduction.