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Ladder relations for a class of matrix valued orthogonal polynomials

Deaño, Alfredo, Eijsvoogel, Bruno, Román, Pablo (2021) Ladder relations for a class of matrix valued orthogonal polynomials. Studies in Applied Mathematics, 146 (2). pp. 463-497. ISSN 0022-2526. (doi:10.1111/sapm.12351) (KAR id:80236)

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Abstract

Using the theory introduced by Casper and Yakimov, we investigate the structure of algebras of differential and difference operators acting on matrix valued orthogonal polynomials (MVOPs) on \(\Bbb R\), and we derive algebraic and differential relations for these MVOPs. A particular case of importance is that of MVOPs with respect to a matrix weight of the form W(x)=e\(^{-v(x)}\)e\(^{xA}\)e\(^{xA*}\) on the real line, where v is a scalar polynomial of even degree with positive leading coefficient and A is a constant matrix.

Item Type: Article
DOI/Identification number: 10.1111/sapm.12351
Uncontrolled keywords: integrable systems, ladder relations, mathematical physics, non–Abelian Toda lattice, orthogonal polynomials
Subjects: Q Science > QA Mathematics (inc Computing science) > QA351 Special functions
Q Science > QA Mathematics (inc Computing science) > QA372 Ordinary differential equations
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Depositing User: Alfredo Deano Cabrera
Date Deposited: 25 Feb 2020 17:58 UTC
Last Modified: 02 Jun 2021 09:30 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/80236 (The current URI for this page, for reference purposes)
Deaño, Alfredo: https://orcid.org/0000-0003-1704-247X
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