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The multicomponent 2D Toda hierarchy: generalized matrix orthogonal polynomials, multiple orthogonal polynomials and Riemann-Hilbert problems

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Álvarez Fernández, Carlos and Fidalgo Prieto, Ulises and Mañas Baena, Manuel (2010) The multicomponent 2D Toda hierarchy: generalized matrix orthogonal polynomials, multiple orthogonal polynomials and Riemann-Hilbert problems. Inverse problems, 26 (5). ISSN 0266-5611

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Official URL: http://dx.doi.org/10.1088/0266-5611/26/5/055009




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.

Uncontrolled Keywords:Discrete kp
Subjects:Sciences > Physics > Physics-Mathematical models
Sciences > Physics > Mathematical physics
ID Code:31499
Deposited On:20 Jul 2015 10:42
Last Modified:10 Dec 2018 15:09

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