Publication: The multicomponent 2D Toda hierarchy: generalized matrix orthogonal polynomials, multiple orthogonal polynomials and Riemann-Hilbert problems
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2010-05
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IOP Publishing
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Abstract
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.
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©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.
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