An Explicit Formula for the Dirac Multiplicities on Lens Spaces

Autores
Boldt, Sebastián; Lauret, Emilio Agustin
Año de publicación
2017
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We present a new description of the spectrum of the (spin-) Dirac operator D on lens spaces. Viewing a spin lens space L as a locally symmetric space Gammaackslash operatorname{Spin}(2m)/operatorname{Spin}(2m-1) and exploiting the representation theory of the operatorname{Spin} groups, we obtain explicit formulas for the multiplicities of the eigenvalues of D in terms of finitely many integer operations. As a consequence, we present conditions for lens spaces to be Dirac isospectral. Tackling classic questions of spectral geometry, we prove with the tools developed that neither spin structures nor isometry classes of lens spaces are spectrally determined by giving infinite families of Dirac isospectral lens spaces. These results are complemented by examples found with the help of a computer.
Fil: Boldt, Sebastián. Humboldt-Universität zu Berlin; Alemania
Fil: Lauret, Emilio Agustin. 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
Dirac Spectrum
Lens Space
Isospectrality
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:11336/59982
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/59982
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling An Explicit Formula for the Dirac Multiplicities on Lens SpacesBoldt, SebastiánLauret, Emilio AgustinDirac SpectrumLens SpaceIsospectralityhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We present a new description of the spectrum of the (spin-) Dirac operator D on lens spaces. Viewing a spin lens space L as a locally symmetric space Gammaackslash operatorname{Spin}(2m)/operatorname{Spin}(2m-1) and exploiting the representation theory of the operatorname{Spin} groups, we obtain explicit formulas for the multiplicities of the eigenvalues of D in terms of finitely many integer operations. As a consequence, we present conditions for lens spaces to be Dirac isospectral. Tackling classic questions of spectral geometry, we prove with the tools developed that neither spin structures nor isometry classes of lens spaces are spectrally determined by giving infinite families of Dirac isospectral lens spaces. These results are complemented by examples found with the help of a computer.Fil: Boldt, Sebastián. Humboldt-Universität zu Berlin; AlemaniaFil: Lauret, Emilio Agustin. 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; ArgentinaSpringer2017-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/zipapplication/pdfhttp://hdl.handle.net/11336/59982Boldt, Sebastián; Lauret, Emilio Agustin; An Explicit Formula for the Dirac Multiplicities on Lens Spaces; Springer; The Journal Of Geometric Analysis; 27; 1; 1-2017; 689-7251050-6926CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs12220-016-9695-xinfo:eu-repo/semantics/altIdentifier/doi/10.1007/s12220-016-9695-xinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:05:09Zoai:ri.conicet.gov.ar:11336/59982instacron: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 10:05:10.227CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv An Explicit Formula for the Dirac Multiplicities on Lens Spaces
title An Explicit Formula for the Dirac Multiplicities on Lens Spaces
spellingShingle An Explicit Formula for the Dirac Multiplicities on Lens Spaces
Boldt, Sebastián
Dirac Spectrum
Lens Space
Isospectrality
title_short An Explicit Formula for the Dirac Multiplicities on Lens Spaces
title_full An Explicit Formula for the Dirac Multiplicities on Lens Spaces
title_fullStr An Explicit Formula for the Dirac Multiplicities on Lens Spaces
title_full_unstemmed An Explicit Formula for the Dirac Multiplicities on Lens Spaces
title_sort An Explicit Formula for the Dirac Multiplicities on Lens Spaces
dc.creator.none.fl_str_mv Boldt, Sebastián
Lauret, Emilio Agustin
author Boldt, Sebastián
author_facet Boldt, Sebastián
Lauret, Emilio Agustin
author_role author
author2 Lauret, Emilio Agustin
author2_role author
dc.subject.none.fl_str_mv Dirac Spectrum
Lens Space
Isospectrality
topic Dirac Spectrum
Lens Space
Isospectrality
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 new description of the spectrum of the (spin-) Dirac operator D on lens spaces. Viewing a spin lens space L as a locally symmetric space Gammaackslash operatorname{Spin}(2m)/operatorname{Spin}(2m-1) and exploiting the representation theory of the operatorname{Spin} groups, we obtain explicit formulas for the multiplicities of the eigenvalues of D in terms of finitely many integer operations. As a consequence, we present conditions for lens spaces to be Dirac isospectral. Tackling classic questions of spectral geometry, we prove with the tools developed that neither spin structures nor isometry classes of lens spaces are spectrally determined by giving infinite families of Dirac isospectral lens spaces. These results are complemented by examples found with the help of a computer.
Fil: Boldt, Sebastián. Humboldt-Universität zu Berlin; Alemania
Fil: Lauret, Emilio Agustin. 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 new description of the spectrum of the (spin-) Dirac operator D on lens spaces. Viewing a spin lens space L as a locally symmetric space Gammaackslash operatorname{Spin}(2m)/operatorname{Spin}(2m-1) and exploiting the representation theory of the operatorname{Spin} groups, we obtain explicit formulas for the multiplicities of the eigenvalues of D in terms of finitely many integer operations. As a consequence, we present conditions for lens spaces to be Dirac isospectral. Tackling classic questions of spectral geometry, we prove with the tools developed that neither spin structures nor isometry classes of lens spaces are spectrally determined by giving infinite families of Dirac isospectral lens spaces. These results are complemented by examples found with the help of a computer.
publishDate 2017
dc.date.none.fl_str_mv 2017-01
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/11336/59982
Boldt, Sebastián; Lauret, Emilio Agustin; An Explicit Formula for the Dirac Multiplicities on Lens Spaces; Springer; The Journal Of Geometric Analysis; 27; 1; 1-2017; 689-725
1050-6926
CONICET Digital
CONICET
url http://hdl.handle.net/11336/59982
identifier_str_mv Boldt, Sebastián; Lauret, Emilio Agustin; An Explicit Formula for the Dirac Multiplicities on Lens Spaces; Springer; The Journal Of Geometric Analysis; 27; 1; 1-2017; 689-725
1050-6926
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://link.springer.com/article/10.1007%2Fs12220-016-9695-x
info:eu-repo/semantics/altIdentifier/doi/10.1007/s12220-016-9695-x
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/zip
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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score 13.070432

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