Matrix-valued orthogonal polynomials related to the quantum analogue of (SU (2) × SU (2) , diag)

Autores
N. Aldenhoven; Koelink, Hendrik Tjerk; Román, Pablo Manuel
Año de publicación
2017
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Matrix-valued spherical functions related to the quantum symmetric pair for the quantum analogue of (SU (2) × SU (2) , diag) are introduced and studied in detail. The quantum symmetric pair is given in terms of a quantised universal enveloping algebra with a coideal subalgebra. The matrix-valued spherical functions give rise to matrix-valued orthogonal polynomials, which are matrix-valued analogues of a subfamily of Askey–Wilson polynomials. For these matrix-valued orthogonal polynomials, a number of properties are derived using this quantum group interpretation: the orthogonality relations from the Schur orthogonality relations, the three-term recurrence relation and the structure of the weight matrix in terms of Chebyshev polynomials from tensor product decompositions, and the matrix-valued Askey–Wilson type q-difference operators from the action of the Casimir elements. A more analytic study of the weight gives an explicit LDU-decomposition in terms of continuous q-ultraspherical polynomials. The LDU-decomposition gives the possibility to find explicit expressions of the matrix entries of the matrix-valued orthogonal polynomials in terms of continuous q-ultraspherical polynomials and q-Racah polynomials.
Fil: N. Aldenhoven. Radboud Universiteit Nijmegen; Países Bajos
Fil: Koelink, Hendrik Tjerk. Radboud Universiteit Nijmegen; Países Bajos
Fil: Román, Pablo Manuel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina
Materia
Continuous Q-Ultraspherical Polynomials
Matrix-Valued Orthogonal Polynomials
Q-Racah Polynomials
Quantum Groups
Quantum Symmetric Pairs
Spherical Functions
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/62509
Acceder
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repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Matrix-valued orthogonal polynomials related to the quantum analogue of (SU (2) × SU (2) , diag)N. AldenhovenKoelink, Hendrik TjerkRomán, Pablo ManuelContinuous Q-Ultraspherical PolynomialsMatrix-Valued Orthogonal PolynomialsQ-Racah PolynomialsQuantum GroupsQuantum Symmetric PairsSpherical Functionshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Matrix-valued spherical functions related to the quantum symmetric pair for the quantum analogue of (SU (2) × SU (2) , diag) are introduced and studied in detail. The quantum symmetric pair is given in terms of a quantised universal enveloping algebra with a coideal subalgebra. The matrix-valued spherical functions give rise to matrix-valued orthogonal polynomials, which are matrix-valued analogues of a subfamily of Askey–Wilson polynomials. For these matrix-valued orthogonal polynomials, a number of properties are derived using this quantum group interpretation: the orthogonality relations from the Schur orthogonality relations, the three-term recurrence relation and the structure of the weight matrix in terms of Chebyshev polynomials from tensor product decompositions, and the matrix-valued Askey–Wilson type q-difference operators from the action of the Casimir elements. A more analytic study of the weight gives an explicit LDU-decomposition in terms of continuous q-ultraspherical polynomials. The LDU-decomposition gives the possibility to find explicit expressions of the matrix entries of the matrix-valued orthogonal polynomials in terms of continuous q-ultraspherical polynomials and q-Racah polynomials.Fil: N. Aldenhoven. Radboud Universiteit Nijmegen; Países BajosFil: Koelink, Hendrik Tjerk. Radboud Universiteit Nijmegen; Países BajosFil: Román, Pablo Manuel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; ArgentinaSpringer2017-06info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/62509N. Aldenhoven; Koelink, Hendrik Tjerk; Román, Pablo Manuel; Matrix-valued orthogonal polynomials related to the quantum analogue of (SU (2) × SU (2) , diag); Springer; Ramanujan Journal; 43; 2; 6-2017; 243-3111382-4090CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1007/s11139-016-9788-yinfo:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s11139-016-9788-yinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T12:09:00Zoai:ri.conicet.gov.ar:11336/62509instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-10-22 12:09:00.955CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Matrix-valued orthogonal polynomials related to the quantum analogue of (SU (2) × SU (2) , diag)
title Matrix-valued orthogonal polynomials related to the quantum analogue of (SU (2) × SU (2) , diag)
spellingShingle Matrix-valued orthogonal polynomials related to the quantum analogue of (SU (2) × SU (2) , diag)
N. Aldenhoven
Continuous Q-Ultraspherical Polynomials
Matrix-Valued Orthogonal Polynomials
Q-Racah Polynomials
Quantum Groups
Quantum Symmetric Pairs
Spherical Functions
title_short Matrix-valued orthogonal polynomials related to the quantum analogue of (SU (2) × SU (2) , diag)
title_full Matrix-valued orthogonal polynomials related to the quantum analogue of (SU (2) × SU (2) , diag)
title_fullStr Matrix-valued orthogonal polynomials related to the quantum analogue of (SU (2) × SU (2) , diag)
title_full_unstemmed Matrix-valued orthogonal polynomials related to the quantum analogue of (SU (2) × SU (2) , diag)
title_sort Matrix-valued orthogonal polynomials related to the quantum analogue of (SU (2) × SU (2) , diag)
dc.creator.none.fl_str_mv N. Aldenhoven
Koelink, Hendrik Tjerk
Román, Pablo Manuel
author N. Aldenhoven
author_facet N. Aldenhoven
Koelink, Hendrik Tjerk
Román, Pablo Manuel
author_role author
author2 Koelink, Hendrik Tjerk
Román, Pablo Manuel
author2_role author
author
dc.subject.none.fl_str_mv Continuous Q-Ultraspherical Polynomials
Matrix-Valued Orthogonal Polynomials
Q-Racah Polynomials
Quantum Groups
Quantum Symmetric Pairs
Spherical Functions
topic Continuous Q-Ultraspherical Polynomials
Matrix-Valued Orthogonal Polynomials
Q-Racah Polynomials
Quantum Groups
Quantum Symmetric Pairs
Spherical Functions
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Matrix-valued spherical functions related to the quantum symmetric pair for the quantum analogue of (SU (2) × SU (2) , diag) are introduced and studied in detail. The quantum symmetric pair is given in terms of a quantised universal enveloping algebra with a coideal subalgebra. The matrix-valued spherical functions give rise to matrix-valued orthogonal polynomials, which are matrix-valued analogues of a subfamily of Askey–Wilson polynomials. For these matrix-valued orthogonal polynomials, a number of properties are derived using this quantum group interpretation: the orthogonality relations from the Schur orthogonality relations, the three-term recurrence relation and the structure of the weight matrix in terms of Chebyshev polynomials from tensor product decompositions, and the matrix-valued Askey–Wilson type q-difference operators from the action of the Casimir elements. A more analytic study of the weight gives an explicit LDU-decomposition in terms of continuous q-ultraspherical polynomials. The LDU-decomposition gives the possibility to find explicit expressions of the matrix entries of the matrix-valued orthogonal polynomials in terms of continuous q-ultraspherical polynomials and q-Racah polynomials.
Fil: N. Aldenhoven. Radboud Universiteit Nijmegen; Países Bajos
Fil: Koelink, Hendrik Tjerk. Radboud Universiteit Nijmegen; Países Bajos
Fil: Román, Pablo Manuel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina
description Matrix-valued spherical functions related to the quantum symmetric pair for the quantum analogue of (SU (2) × SU (2) , diag) are introduced and studied in detail. The quantum symmetric pair is given in terms of a quantised universal enveloping algebra with a coideal subalgebra. The matrix-valued spherical functions give rise to matrix-valued orthogonal polynomials, which are matrix-valued analogues of a subfamily of Askey–Wilson polynomials. For these matrix-valued orthogonal polynomials, a number of properties are derived using this quantum group interpretation: the orthogonality relations from the Schur orthogonality relations, the three-term recurrence relation and the structure of the weight matrix in terms of Chebyshev polynomials from tensor product decompositions, and the matrix-valued Askey–Wilson type q-difference operators from the action of the Casimir elements. A more analytic study of the weight gives an explicit LDU-decomposition in terms of continuous q-ultraspherical polynomials. The LDU-decomposition gives the possibility to find explicit expressions of the matrix entries of the matrix-valued orthogonal polynomials in terms of continuous q-ultraspherical polynomials and q-Racah polynomials.
publishDate 2017
dc.date.none.fl_str_mv 2017-06
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/62509
N. Aldenhoven; Koelink, Hendrik Tjerk; Román, Pablo Manuel; Matrix-valued orthogonal polynomials related to the quantum analogue of (SU (2) × SU (2) , diag); Springer; Ramanujan Journal; 43; 2; 6-2017; 243-311
1382-4090
CONICET Digital
CONICET
url http://hdl.handle.net/11336/62509
identifier_str_mv N. Aldenhoven; Koelink, Hendrik Tjerk; Román, Pablo Manuel; Matrix-valued orthogonal polynomials related to the quantum analogue of (SU (2) × SU (2) , diag); Springer; Ramanujan Journal; 43; 2; 6-2017; 243-311
1382-4090
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1007/s11139-016-9788-y
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s11139-016-9788-y
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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