A note on étale representations from nilpotent orbits

Autores
Dietrich, Heiko; Globke, Wolfgang; Origlia, Marcos Miguel
Año de publicación
2022
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
A linear étale representation of a complex algebraic group G is given by a complex algebraic G-module V such that G has a Zariski-open orbit in V and. A current line of research investigates which reductive algebraic groups admit such étale representations, with a focus on understanding common features of étale representations. One source of new examples arises from the classification theory of nilpotent orbits in semisimple Lie algebras. We survey what is known about reductive algebraic groups with étale representations and then discuss two classical constructions for nilpotent orbit classifications due to Vinberg and to Bala and Carter. We determine which reductive groups and étale representations arise in these constructions and we work out in detail the relation between these two constructions.
Fil: Dietrich, Heiko. Monash University; Australia
Fil: Globke, Wolfgang. Universidad de Viena; Austria
Fil: Origlia, Marcos Miguel. Monash University; Australia. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. 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
MATHEMATICS
20G05 17B10 22E46
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/203134
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/203134
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling A note on étale representations from nilpotent orbitsDietrich, HeikoGlobke, WolfgangOriglia, Marcos MiguelMATHEMATICS20G05 17B10 22E46https://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1A linear étale representation of a complex algebraic group G is given by a complex algebraic G-module V such that G has a Zariski-open orbit in V and. A current line of research investigates which reductive algebraic groups admit such étale representations, with a focus on understanding common features of étale representations. One source of new examples arises from the classification theory of nilpotent orbits in semisimple Lie algebras. We survey what is known about reductive algebraic groups with étale representations and then discuss two classical constructions for nilpotent orbit classifications due to Vinberg and to Bala and Carter. We determine which reductive groups and étale representations arise in these constructions and we work out in detail the relation between these two constructions.Fil: Dietrich, Heiko. Monash University; AustraliaFil: Globke, Wolfgang. Universidad de Viena; AustriaFil: Origlia, Marcos Miguel. Monash University; Australia. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. 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; ArgentinaAustralian Mathematics Publ Assoc Inc2022-08info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/203134Dietrich, Heiko; Globke, Wolfgang; Origlia, Marcos Miguel; A note on étale representations from nilpotent orbits; Australian Mathematics Publ Assoc Inc; Bulletin Of The Australian Mathematical Society; 106; 1; 8-2022; 113-1250004-9727CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1017/S0004972721001283info:eu-repo/semantics/altIdentifier/url/https://www.cambridge.org/core/journals/bulletin-of-the-australian-mathematical-society/article/note-on-etale-representations-from-nilpotent-orbits/6F4AE084D3DC709D123480E3AAF1FAA2info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:18:01Zoai:ri.conicet.gov.ar:11336/203134instacron: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 10:18:01.507CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv A note on étale representations from nilpotent orbits
title A note on étale representations from nilpotent orbits
spellingShingle A note on étale representations from nilpotent orbits
Dietrich, Heiko
MATHEMATICS
20G05 17B10 22E46
title_short A note on étale representations from nilpotent orbits
title_full A note on étale representations from nilpotent orbits
title_fullStr A note on étale representations from nilpotent orbits
title_full_unstemmed A note on étale representations from nilpotent orbits
title_sort A note on étale representations from nilpotent orbits
dc.creator.none.fl_str_mv Dietrich, Heiko
Globke, Wolfgang
Origlia, Marcos Miguel
author Dietrich, Heiko
author_facet Dietrich, Heiko
Globke, Wolfgang
Origlia, Marcos Miguel
author_role author
author2 Globke, Wolfgang
Origlia, Marcos Miguel
author2_role author
author
dc.subject.none.fl_str_mv MATHEMATICS
20G05 17B10 22E46
topic MATHEMATICS
20G05 17B10 22E46
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv A linear étale representation of a complex algebraic group G is given by a complex algebraic G-module V such that G has a Zariski-open orbit in V and. A current line of research investigates which reductive algebraic groups admit such étale representations, with a focus on understanding common features of étale representations. One source of new examples arises from the classification theory of nilpotent orbits in semisimple Lie algebras. We survey what is known about reductive algebraic groups with étale representations and then discuss two classical constructions for nilpotent orbit classifications due to Vinberg and to Bala and Carter. We determine which reductive groups and étale representations arise in these constructions and we work out in detail the relation between these two constructions.
Fil: Dietrich, Heiko. Monash University; Australia
Fil: Globke, Wolfgang. Universidad de Viena; Austria
Fil: Origlia, Marcos Miguel. Monash University; Australia. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. 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 A linear étale representation of a complex algebraic group G is given by a complex algebraic G-module V such that G has a Zariski-open orbit in V and. A current line of research investigates which reductive algebraic groups admit such étale representations, with a focus on understanding common features of étale representations. One source of new examples arises from the classification theory of nilpotent orbits in semisimple Lie algebras. We survey what is known about reductive algebraic groups with étale representations and then discuss two classical constructions for nilpotent orbit classifications due to Vinberg and to Bala and Carter. We determine which reductive groups and étale representations arise in these constructions and we work out in detail the relation between these two constructions.
publishDate 2022
dc.date.none.fl_str_mv 2022-08
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/11336/203134
Dietrich, Heiko; Globke, Wolfgang; Origlia, Marcos Miguel; A note on étale representations from nilpotent orbits; Australian Mathematics Publ Assoc Inc; Bulletin Of The Australian Mathematical Society; 106; 1; 8-2022; 113-125
0004-9727
CONICET Digital
CONICET
url http://hdl.handle.net/11336/203134
identifier_str_mv Dietrich, Heiko; Globke, Wolfgang; Origlia, Marcos Miguel; A note on étale representations from nilpotent orbits; Australian Mathematics Publ Assoc Inc; Bulletin Of The Australian Mathematical Society; 106; 1; 8-2022; 113-125
0004-9727
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1017/S0004972721001283
info:eu-repo/semantics/altIdentifier/url/https://www.cambridge.org/core/journals/bulletin-of-the-australian-mathematical-society/article/note-on-etale-representations-from-nilpotent-orbits/6F4AE084D3DC709D123480E3AAF1FAA2
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Australian Mathematics Publ Assoc Inc
publisher.none.fl_str_mv Australian Mathematics Publ Assoc Inc
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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