The Algebra of differential operators for a matrix weight: An ultraspherical example
- Autores
- Zurrián, Ignacio Nahuel
- Año de publicación
- 2017
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- In this article we study in detail algebraic properties of the algebra D(W) of differential operators associated to a matrix weight of Gegenbauer type. We prove that two secondorder operators generate the algebra, indeed D(W) is isomorphic to the free algebra generated by two elements subject to certain relations. Also, the center is isomorphic to the affine algebra of a singular rational curve. The algebra D(W) is a finitely generated torsion-free module over its center, but it is not flat and therefore it is not projective. This is the second detailed study of an algebra D(W) and the first one coming from spherical functions and group representations. We prove that the algebras for different Gegenbauer weights and the algebras studied previously, related to Hermite weights, are isomorphic to each other. We give some general results that allow us to regard the algebra D(W) as the centralizer of its center in the Weyl algebra. We do believe that this should hold for any irreducible weight and the case considered in this article represents a good step in this direction.
Fil: Zurrián, Ignacio Nahuel. Pontificia Universidad Católica de Chile; Chile. 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 weights
- Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
- Repositorio
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/58369
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The Algebra of differential operators for a matrix weight: An ultraspherical exampleZurrián, Ignacio Nahuelmatrix weightshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this article we study in detail algebraic properties of the algebra D(W) of differential operators associated to a matrix weight of Gegenbauer type. We prove that two secondorder operators generate the algebra, indeed D(W) is isomorphic to the free algebra generated by two elements subject to certain relations. Also, the center is isomorphic to the affine algebra of a singular rational curve. The algebra D(W) is a finitely generated torsion-free module over its center, but it is not flat and therefore it is not projective. This is the second detailed study of an algebra D(W) and the first one coming from spherical functions and group representations. We prove that the algebras for different Gegenbauer weights and the algebras studied previously, related to Hermite weights, are isomorphic to each other. We give some general results that allow us to regard the algebra D(W) as the centralizer of its center in the Weyl algebra. We do believe that this should hold for any irreducible weight and the case considered in this article represents a good step in this direction.Fil: Zurrián, Ignacio Nahuel. Pontificia Universidad Católica de Chile; Chile. 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; ArgentinaOxford University Press2017-04info: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/11336/58369Zurrián, Ignacio Nahuel; The Algebra of differential operators for a matrix weight: An ultraspherical example; Oxford University Press; International Mathematics Research Notices; 2017; 8; 4-2017; 2402-24301073-7928CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1093/imrn/rnw104info:eu-repo/semantics/altIdentifier/url/https://academic.oup.com/imrn/article-abstract/2017/8/2402/3056814info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1505.03321info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:07:12Zoai:ri.conicet.gov.ar:11336/58369instacron: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 10:07:12.742CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse |
dc.title.none.fl_str_mv |
The Algebra of differential operators for a matrix weight: An ultraspherical example |
title |
The Algebra of differential operators for a matrix weight: An ultraspherical example |
spellingShingle |
The Algebra of differential operators for a matrix weight: An ultraspherical example Zurrián, Ignacio Nahuel matrix weights |
title_short |
The Algebra of differential operators for a matrix weight: An ultraspherical example |
title_full |
The Algebra of differential operators for a matrix weight: An ultraspherical example |
title_fullStr |
The Algebra of differential operators for a matrix weight: An ultraspherical example |
title_full_unstemmed |
The Algebra of differential operators for a matrix weight: An ultraspherical example |
title_sort |
The Algebra of differential operators for a matrix weight: An ultraspherical example |
dc.creator.none.fl_str_mv |
Zurrián, Ignacio Nahuel |
author |
Zurrián, Ignacio Nahuel |
author_facet |
Zurrián, Ignacio Nahuel |
author_role |
author |
dc.subject.none.fl_str_mv |
matrix weights |
topic |
matrix weights |
purl_subject.fl_str_mv |
https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
dc.description.none.fl_txt_mv |
In this article we study in detail algebraic properties of the algebra D(W) of differential operators associated to a matrix weight of Gegenbauer type. We prove that two secondorder operators generate the algebra, indeed D(W) is isomorphic to the free algebra generated by two elements subject to certain relations. Also, the center is isomorphic to the affine algebra of a singular rational curve. The algebra D(W) is a finitely generated torsion-free module over its center, but it is not flat and therefore it is not projective. This is the second detailed study of an algebra D(W) and the first one coming from spherical functions and group representations. We prove that the algebras for different Gegenbauer weights and the algebras studied previously, related to Hermite weights, are isomorphic to each other. We give some general results that allow us to regard the algebra D(W) as the centralizer of its center in the Weyl algebra. We do believe that this should hold for any irreducible weight and the case considered in this article represents a good step in this direction. Fil: Zurrián, Ignacio Nahuel. Pontificia Universidad Católica de Chile; Chile. 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 |
In this article we study in detail algebraic properties of the algebra D(W) of differential operators associated to a matrix weight of Gegenbauer type. We prove that two secondorder operators generate the algebra, indeed D(W) is isomorphic to the free algebra generated by two elements subject to certain relations. Also, the center is isomorphic to the affine algebra of a singular rational curve. The algebra D(W) is a finitely generated torsion-free module over its center, but it is not flat and therefore it is not projective. This is the second detailed study of an algebra D(W) and the first one coming from spherical functions and group representations. We prove that the algebras for different Gegenbauer weights and the algebras studied previously, related to Hermite weights, are isomorphic to each other. We give some general results that allow us to regard the algebra D(W) as the centralizer of its center in the Weyl algebra. We do believe that this should hold for any irreducible weight and the case considered in this article represents a good step in this direction. |
publishDate |
2017 |
dc.date.none.fl_str_mv |
2017-04 |
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/11336/58369 Zurrián, Ignacio Nahuel; The Algebra of differential operators for a matrix weight: An ultraspherical example; Oxford University Press; International Mathematics Research Notices; 2017; 8; 4-2017; 2402-2430 1073-7928 CONICET Digital CONICET |
url |
http://hdl.handle.net/11336/58369 |
identifier_str_mv |
Zurrián, Ignacio Nahuel; The Algebra of differential operators for a matrix weight: An ultraspherical example; Oxford University Press; International Mathematics Research Notices; 2017; 8; 4-2017; 2402-2430 1073-7928 CONICET Digital CONICET |
dc.language.none.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
info:eu-repo/semantics/altIdentifier/doi/10.1093/imrn/rnw104 info:eu-repo/semantics/altIdentifier/url/https://academic.oup.com/imrn/article-abstract/2017/8/2402/3056814 info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1505.03321 |
dc.rights.none.fl_str_mv |
info:eu-repo/semantics/openAccess https://creativecommons.org/licenses/by-nc-sa/2.5/ar/ |
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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 |
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Oxford University Press |
publisher.none.fl_str_mv |
Oxford University Press |
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reponame:CONICET Digital (CONICET) instname:Consejo Nacional de Investigaciones Científicas y Técnicas |
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Consejo Nacional de Investigaciones Científicas y Técnicas |
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CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas |
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dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar |
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