# Properties of matrix orthogonal polynomials via their Riemann-Hilbert characterization

@article{Grunbaum2011PropertiesOM, title={Properties of matrix orthogonal polynomials via their Riemann-Hilbert characterization}, author={F. Alberto Grunbaum and Manuel Dom{\'i}nguez de la Iglesia and Andrei Mart{\'i}nez-Finkelshtein}, journal={Symmetry Integrability and Geometry-methods and Applications}, year={2011}, volume={7}, pages={098} }

We give a Riemann{Hilbert approach to the theory of matrix orthogonal poly- nomials. We will focus on the algebraic aspects of the problem, obtaining difference and differential relations satisfied by the corresponding orthogonal polynomials. We will show that in the matrix case there is some extra freedom that allows us to obtain a family of lad- der operators, some of them of 0-th order, something that is not possible in the scalar case. The combination of the ladder operators will lead to a…

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