Matrix Jacobi biorthogonal polynomials via Riemann–Hilbert problem

We consider matrix orthogonal polynomials related to Jacobi type matrices of weights that can be defined in terms of a given matrix Pearson equation. Stating a Riemann–Hilbert problem we can derive first and second order differential-difference relations that these matrix orthogonal polynomials and the second kind functions associated to them verify. For the corresponding matrix recurrence coefficients, non-Abelian extensions of a family of discrete Painlevé d-P I V IV equations are obtained for the three term recurrence relation coefficients.