Matrix valued classical pairs related to compact gelfand pairs of rank one

Autores
van Pruijssen, Maarten; Román, Pablo Manuel
Año de publicación
2014
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We present a method to obtain infinitely many examples of pairs (W, D) consisting of a matrix weight W in one variable and a symmetric second-order differential operator D. The method is based on a uniform construction of matrix valued polynomials starting from compact Gelfand pairs (G, K) of rank one and a suitable irreducible K-representation. The heart of the construction is the existence of a suitable base change Ψ0. We analyze the base change and derive several properties. The most important one is that Ψ0satisfies a first-order differential equation which enables us to compute the radial part of the Casimir operator of the group G as soon as we have an explicit expression for Ψ0. The weight W is also determined by Ψ0. We provide an algorithm to calculate Ψ0explicitly. For the pair (USp(2n), USp(2n - 2) × USp(2)) we have implemented the algorithm in GAP so that individual pairs (W, D) can be calculated explicitly. Finally we classify the Gelfand pairs (G, K) and the K-representations that yield pairs (W, D) of size 2 × 2 and we provide explicit expressions for most of these cases.
Fil: van Pruijssen, Maarten. Universität Paderborn; Alemania
Fil: Román, Pablo Manuel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina
Materia
MATRIX VALUED CLASSICAL PAIRS
MULTIPLICITY FREE BRANCHING
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:11336/58331
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/58331
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Matrix valued classical pairs related to compact gelfand pairs of rank onevan Pruijssen, MaartenRomán, Pablo ManuelMATRIX VALUED CLASSICAL PAIRSMULTIPLICITY FREE BRANCHINGhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We present a method to obtain infinitely many examples of pairs (W, D) consisting of a matrix weight W in one variable and a symmetric second-order differential operator D. The method is based on a uniform construction of matrix valued polynomials starting from compact Gelfand pairs (G, K) of rank one and a suitable irreducible K-representation. The heart of the construction is the existence of a suitable base change Ψ0. We analyze the base change and derive several properties. The most important one is that Ψ0satisfies a first-order differential equation which enables us to compute the radial part of the Casimir operator of the group G as soon as we have an explicit expression for Ψ0. The weight W is also determined by Ψ0. We provide an algorithm to calculate Ψ0explicitly. For the pair (USp(2n), USp(2n - 2) × USp(2)) we have implemented the algorithm in GAP so that individual pairs (W, D) can be calculated explicitly. Finally we classify the Gelfand pairs (G, K) and the K-representations that yield pairs (W, D) of size 2 × 2 and we provide explicit expressions for most of these cases.Fil: van Pruijssen, Maarten. Universität Paderborn; AlemaniaFil: Román, Pablo Manuel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; ArgentinaNatl Acad Sci Ukraine2014-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/58331van Pruijssen, Maarten; Román, Pablo Manuel; Matrix valued classical pairs related to compact gelfand pairs of rank one; Natl Acad Sci Ukraine; Symmetry, Integrability And Geometry; 10; 113; 12-2014; 1-281815-0659CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.emis.de/journals/SIGMA/2014/113/info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1312.6577info:eu-repo/semantics/altIdentifier/doi/10.3842/SIGMA.2014.113info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:46:59Zoai:ri.conicet.gov.ar:11336/58331instacron: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:34982025-09-29 10:47:00.107CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Matrix valued classical pairs related to compact gelfand pairs of rank one
title Matrix valued classical pairs related to compact gelfand pairs of rank one
spellingShingle Matrix valued classical pairs related to compact gelfand pairs of rank one
van Pruijssen, Maarten
MATRIX VALUED CLASSICAL PAIRS
MULTIPLICITY FREE BRANCHING
title_short Matrix valued classical pairs related to compact gelfand pairs of rank one
title_full Matrix valued classical pairs related to compact gelfand pairs of rank one
title_fullStr Matrix valued classical pairs related to compact gelfand pairs of rank one
title_full_unstemmed Matrix valued classical pairs related to compact gelfand pairs of rank one
title_sort Matrix valued classical pairs related to compact gelfand pairs of rank one
dc.creator.none.fl_str_mv van Pruijssen, Maarten
Román, Pablo Manuel
author van Pruijssen, Maarten
author_facet van Pruijssen, Maarten
Román, Pablo Manuel
author_role author
author2 Román, Pablo Manuel
author2_role author
dc.subject.none.fl_str_mv MATRIX VALUED CLASSICAL PAIRS
MULTIPLICITY FREE BRANCHING
topic MATRIX VALUED CLASSICAL PAIRS
MULTIPLICITY FREE BRANCHING
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We present a method to obtain infinitely many examples of pairs (W, D) consisting of a matrix weight W in one variable and a symmetric second-order differential operator D. The method is based on a uniform construction of matrix valued polynomials starting from compact Gelfand pairs (G, K) of rank one and a suitable irreducible K-representation. The heart of the construction is the existence of a suitable base change Ψ0. We analyze the base change and derive several properties. The most important one is that Ψ0satisfies a first-order differential equation which enables us to compute the radial part of the Casimir operator of the group G as soon as we have an explicit expression for Ψ0. The weight W is also determined by Ψ0. We provide an algorithm to calculate Ψ0explicitly. For the pair (USp(2n), USp(2n - 2) × USp(2)) we have implemented the algorithm in GAP so that individual pairs (W, D) can be calculated explicitly. Finally we classify the Gelfand pairs (G, K) and the K-representations that yield pairs (W, D) of size 2 × 2 and we provide explicit expressions for most of these cases.
Fil: van Pruijssen, Maarten. Universität Paderborn; Alemania
Fil: Román, Pablo Manuel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina
description We present a method to obtain infinitely many examples of pairs (W, D) consisting of a matrix weight W in one variable and a symmetric second-order differential operator D. The method is based on a uniform construction of matrix valued polynomials starting from compact Gelfand pairs (G, K) of rank one and a suitable irreducible K-representation. The heart of the construction is the existence of a suitable base change Ψ0. We analyze the base change and derive several properties. The most important one is that Ψ0satisfies a first-order differential equation which enables us to compute the radial part of the Casimir operator of the group G as soon as we have an explicit expression for Ψ0. The weight W is also determined by Ψ0. We provide an algorithm to calculate Ψ0explicitly. For the pair (USp(2n), USp(2n - 2) × USp(2)) we have implemented the algorithm in GAP so that individual pairs (W, D) can be calculated explicitly. Finally we classify the Gelfand pairs (G, K) and the K-representations that yield pairs (W, D) of size 2 × 2 and we provide explicit expressions for most of these cases.
publishDate 2014
dc.date.none.fl_str_mv 2014-12
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/11336/58331
van Pruijssen, Maarten; Román, Pablo Manuel; Matrix valued classical pairs related to compact gelfand pairs of rank one; Natl Acad Sci Ukraine; Symmetry, Integrability And Geometry; 10; 113; 12-2014; 1-28
1815-0659
CONICET Digital
CONICET
url http://hdl.handle.net/11336/58331
identifier_str_mv van Pruijssen, Maarten; Román, Pablo Manuel; Matrix valued classical pairs related to compact gelfand pairs of rank one; Natl Acad Sci Ukraine; Symmetry, Integrability And Geometry; 10; 113; 12-2014; 1-28
1815-0659
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://www.emis.de/journals/SIGMA/2014/113/
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1312.6577
info:eu-repo/semantics/altIdentifier/doi/10.3842/SIGMA.2014.113
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
dc.publisher.none.fl_str_mv Natl Acad Sci Ukraine
publisher.none.fl_str_mv Natl Acad Sci Ukraine
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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score 13.070432

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