Orthogonal functions related to Lax pairs in Lie algebras

Wolter Groenevelt; Erik Koelink

doi:10.1007/s11139-021-00424-9

Orthogonal functions related to Lax pairs in Lie algebras

Wolter Groenevelt, Erik Koelink

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Abstract

We study a Lax pair in a 2-parameter Lie algebra in various representations. The overlap coefficients of the eigenfunctions of L and the standard basis are given in terms of orthogonal polynomials and orthogonal functions. Eigenfunctions for the operator L for a Lax pair for sl(d+ 1 , C) is studied in certain representations.

Original language	English
Pages (from-to)	445-474
Number of pages	30
Journal	The Ramanujan Journal: an international journal devoted to areas of mathematics influenced by Ramanujan
Volume	61 (2023)
Issue number	2
DOIs	https://doi.org/10.1007/s11139-021-00424-9
Publication status	Published - 2021

Keywords

Orthogonal polynomials
Special functions
Toda lattice

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10.1007/s11139-021-00424-9

s11139-021-00424-9Final published version, 396 KBLicence: CC BY

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AU - Koelink, Erik

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AB - We study a Lax pair in a 2-parameter Lie algebra in various representations. The overlap coefficients of the eigenfunctions of L and the standard basis are given in terms of orthogonal polynomials and orthogonal functions. Eigenfunctions for the operator L for a Lax pair for sl(d+ 1 , C) is studied in certain representations.

KW - Orthogonal polynomials

KW - Special functions

KW - Toda lattice

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U2 - 10.1007/s11139-021-00424-9

DO - 10.1007/s11139-021-00424-9

M3 - Article

AN - SCOPUS:85107481694

SN - 1382-4090

VL - 61 (2023)

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JO - The Ramanujan Journal: an international journal devoted to areas of mathematics influenced by Ramanujan

JF - The Ramanujan Journal: an international journal devoted to areas of mathematics influenced by Ramanujan

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ER -

Orthogonal functions related to Lax pairs in Lie algebras

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