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dc.contributor.author
Zurrián, Ignacio Nahuel
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dc.date.available
2018-09-05T15:35:06Z
dc.date.issued
2017-04
dc.identifier.citation
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
dc.identifier.issn
1073-7928
dc.identifier.uri
http://hdl.handle.net/11336/58369
dc.description.abstract
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.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
Oxford University Press
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dc.rights
info:eu-repo/semantics/openAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
Matrix Weights
dc.subject.classification
Matemática Pura
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dc.subject.classification
Matemáticas
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dc.subject.classification
CIENCIAS NATURALES Y EXACTAS
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dc.title
The Algebra of differential operators for a matrix weight: An ultraspherical example
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2018-09-04T21:37:45Z
dc.journal.volume
2017
dc.journal.number
8
dc.journal.pagination
2402-2430
dc.journal.pais
Reino Unido
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dc.journal.ciudad
Oxford
dc.description.fil
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
dc.journal.title
International Mathematics Research Notices
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dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.1093/imrn/rnw104
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://academic.oup.com/imrn/article-abstract/2017/8/2402/3056814
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1505.03321
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