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Ladder relations for a class of matrix valued orthogonal polynomials

Deaño, Alfredo, Eijsvoogel, Bruno, Román, Pablo (2019) Ladder relations for a class of matrix valued orthogonal polynomials. Communications in Mathematical Physics, . ISSN 0010-3616. (Submitted) (KAR id:80236)

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Official URL
https://arxiv.org/abs/1907.07447

Abstract

In this paper we study algebraic and differential relations for matrix valued orthogonal polynomials (MVOPs) defined on the real line. Using recent results by Casper and Yakimov, we investigate MVOPs with respect to an exponential matrix weight on the real line. We obtain ladder operators, discrete string equations for the recurrence coefficients and multi-time Toda equations for deformations with respect to parameters in the weight, and we show that the Lie algebra generated by the ladder operators is finite dimensional. Hermite-type matrix valued weights are studied in detail: in this case the weight is characterized by the ladder operators, and the Lie algebra generated by them can be extended to a Lie algebra that is isomorphic to the standard Harmonic oscillator algebra. Freud-type matrix weights are also discussed. Finally, we establish the link between these ladder relations and those considered previously by A. Durán and M. Ismail.

Item Type: Article
Subjects: Q Science > QA Mathematics (inc Computing science) > QA351 Special functions
Q Science > QA Mathematics (inc Computing science) > QA372 Ordinary differential equations
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Applied Mathematics
Depositing User: Alfredo Deano Cabrera
Date Deposited: 25 Feb 2020 17:58 UTC
Last Modified: 26 Feb 2020 15:34 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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