Álvarez Fernández, CarlosFidalgo Prieto, UlisesMañas Baena, Manuel Enrique2023-06-202023-06-202010-050266-561110.1088/0266-5611/26/5/055009https://hdl.handle.net/20.500.14352/44699©IOP Publishing. For financial support MM thanks the Spanish Ministerio de Ciencia e Innovacion, research project FIS2008-00200 and UF thanks the SFRH/BPD/62947/2009, Fundaçao para a Ciéncia e ˆ a Tecnologia of Portugal, PT2009-0031, Acciones Integradas Portugal, Ministerio de Ciencia e Innovacion de España, and MTM2009-12740-C03-01. Ministerio de Ciencia e Innovación de Espana. MM acknowledges different clarifying discussions with Dr Mattia Caffasso, Prof. Pierre van Moerbeke, Prof Luis Mart´ınez Alonso and Prof David Gomez-Ullate.We consider the relation of the multicomponent 2D Toda hierarchy with the matrix orthogonal and biorthogonal polynomials. The multi-graded Hankel reduction of this hierarchy is considered and the corresponding generalized matrix orthogonal polynomials are studied. In particular, for these polynomials we consider the recursion relations, and for rank 1 weights its relation with multiple orthogonal polynomials of mixed type with a type II normalization and the corresponding link with a Riemann-Hilbert problem.engjournal articlehttp://dx.doi.org/10.1088/0266-5611/26/5/055009http://iopscience.iop.orghttp://arxiv.org/abs/0911.0941open access51-73Discrete kpFísica-Modelos matemáticosFísica matemática