A special class of rank 10 and 11 Coxeter groups

Autores
Henneaux, Marc; Leston, Mauricio; Persson, Daniel; Spindel, Philippe
Año de publicación
2007
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In the course of investigating regular subalgebras of E10(10) related to cosmological solutions of 11-dimensional supergravity supporting an electric 4-form field, a class of rank 10 Coxeter subgroups of the Weyl group of E10(10) was uncovered (hep-th/0606123). These Coxeter groups all share the property that their Coxeter graphs have incidence index 3, i.e. that each node is incident to three and only three single lines. Furthermore, the Coxeter exponents are either 2 or 3, but never ∞. We here go beyond subgroups of the Weyl group of E10(10) and classify all rank 10 Coxeter graphs with these properties. We find 21 distinct Coxeter groups of which 7 were already described in hep-th/0606123. Moreover, we extend the classification to the rank 11 case and we find 252 inequivalent rank 11 Coxeter groups with incidence index 4, of which at least 28 can be regularly embedded into E11(11) .
Fil: Henneaux, Marc. Universite Libre de Bruxelles; Bélgica
Fil: Leston, Mauricio. Consejo Nacional de Investigaciónes Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Astronomía y Física del Espacio. - Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Astronomía y Física del Espacio; Argentina. Vrije Unviversiteit Brussel; Bélgica
Fil: Persson, Daniel. Universite Libre de Bruxelles; Bélgica
Fil: Spindel, Philippe. Acad´emie Wallonie-Bruxelles; Bélgica
Materia
HYDDEN SYMMETRIES
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:11336/20825
Acceder
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network_name_str CONICET Digital (CONICET)
spelling A special class of rank 10 and 11 Coxeter groupsHenneaux, MarcLeston, MauricioPersson, DanielSpindel, PhilippeHYDDEN SYMMETRIEShttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1In the course of investigating regular subalgebras of E10(10) related to cosmological solutions of 11-dimensional supergravity supporting an electric 4-form field, a class of rank 10 Coxeter subgroups of the Weyl group of E10(10) was uncovered (hep-th/0606123). These Coxeter groups all share the property that their Coxeter graphs have incidence index 3, i.e. that each node is incident to three and only three single lines. Furthermore, the Coxeter exponents are either 2 or 3, but never ∞. We here go beyond subgroups of the Weyl group of E10(10) and classify all rank 10 Coxeter graphs with these properties. We find 21 distinct Coxeter groups of which 7 were already described in hep-th/0606123. Moreover, we extend the classification to the rank 11 case and we find 252 inequivalent rank 11 Coxeter groups with incidence index 4, of which at least 28 can be regularly embedded into E11(11) .Fil: Henneaux, Marc. Universite Libre de Bruxelles; BélgicaFil: Leston, Mauricio. Consejo Nacional de Investigaciónes Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Astronomía y Física del Espacio. - Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Astronomía y Física del Espacio; Argentina. Vrije Unviversiteit Brussel; BélgicaFil: Persson, Daniel. Universite Libre de Bruxelles; BélgicaFil: Spindel, Philippe. Acad´emie Wallonie-Bruxelles; BélgicaAmerican Institute of Physics2007-12info: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/11336/20825Henneaux, Marc; Leston, Mauricio; Persson, Daniel; Spindel, Philippe; A special class of rank 10 and 11 Coxeter groups; American Institute of Physics; Journal Of Mathematical Physics; 48; 5; 12-2007; 1-12; 0535120022-2488CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://aip.scitation.org/doi/10.1063/1.2738754info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/hep-th/0610278info:eu-repo/semantics/altIdentifier/doi/10.1063/1.2738754info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:51:37Zoai:ri.conicet.gov.ar:11336/20825instacron: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:34982025-09-03 09:51:37.695CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv A special class of rank 10 and 11 Coxeter groups
title A special class of rank 10 and 11 Coxeter groups
spellingShingle A special class of rank 10 and 11 Coxeter groups
Henneaux, Marc
HYDDEN SYMMETRIES
title_short A special class of rank 10 and 11 Coxeter groups
title_full A special class of rank 10 and 11 Coxeter groups
title_fullStr A special class of rank 10 and 11 Coxeter groups
title_full_unstemmed A special class of rank 10 and 11 Coxeter groups
title_sort A special class of rank 10 and 11 Coxeter groups
dc.creator.none.fl_str_mv Henneaux, Marc
Leston, Mauricio
Persson, Daniel
Spindel, Philippe
author Henneaux, Marc
author_facet Henneaux, Marc
Leston, Mauricio
Persson, Daniel
Spindel, Philippe
author_role author
author2 Leston, Mauricio
Persson, Daniel
Spindel, Philippe
author2_role author
author
author
dc.subject.none.fl_str_mv HYDDEN SYMMETRIES
topic HYDDEN SYMMETRIES
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In the course of investigating regular subalgebras of E10(10) related to cosmological solutions of 11-dimensional supergravity supporting an electric 4-form field, a class of rank 10 Coxeter subgroups of the Weyl group of E10(10) was uncovered (hep-th/0606123). These Coxeter groups all share the property that their Coxeter graphs have incidence index 3, i.e. that each node is incident to three and only three single lines. Furthermore, the Coxeter exponents are either 2 or 3, but never ∞. We here go beyond subgroups of the Weyl group of E10(10) and classify all rank 10 Coxeter graphs with these properties. We find 21 distinct Coxeter groups of which 7 were already described in hep-th/0606123. Moreover, we extend the classification to the rank 11 case and we find 252 inequivalent rank 11 Coxeter groups with incidence index 4, of which at least 28 can be regularly embedded into E11(11) .
Fil: Henneaux, Marc. Universite Libre de Bruxelles; Bélgica
Fil: Leston, Mauricio. Consejo Nacional de Investigaciónes Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Astronomía y Física del Espacio. - Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Astronomía y Física del Espacio; Argentina. Vrije Unviversiteit Brussel; Bélgica
Fil: Persson, Daniel. Universite Libre de Bruxelles; Bélgica
Fil: Spindel, Philippe. Acad´emie Wallonie-Bruxelles; Bélgica
description In the course of investigating regular subalgebras of E10(10) related to cosmological solutions of 11-dimensional supergravity supporting an electric 4-form field, a class of rank 10 Coxeter subgroups of the Weyl group of E10(10) was uncovered (hep-th/0606123). These Coxeter groups all share the property that their Coxeter graphs have incidence index 3, i.e. that each node is incident to three and only three single lines. Furthermore, the Coxeter exponents are either 2 or 3, but never ∞. We here go beyond subgroups of the Weyl group of E10(10) and classify all rank 10 Coxeter graphs with these properties. We find 21 distinct Coxeter groups of which 7 were already described in hep-th/0606123. Moreover, we extend the classification to the rank 11 case and we find 252 inequivalent rank 11 Coxeter groups with incidence index 4, of which at least 28 can be regularly embedded into E11(11) .
publishDate 2007
dc.date.none.fl_str_mv 2007-12
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/11336/20825
Henneaux, Marc; Leston, Mauricio; Persson, Daniel; Spindel, Philippe; A special class of rank 10 and 11 Coxeter groups; American Institute of Physics; Journal Of Mathematical Physics; 48; 5; 12-2007; 1-12; 053512
0022-2488
CONICET Digital
CONICET
url http://hdl.handle.net/11336/20825
identifier_str_mv Henneaux, Marc; Leston, Mauricio; Persson, Daniel; Spindel, Philippe; A special class of rank 10 and 11 Coxeter groups; American Institute of Physics; Journal Of Mathematical Physics; 48; 5; 12-2007; 1-12; 053512
0022-2488
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://aip.scitation.org/doi/10.1063/1.2738754
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/hep-th/0610278
info:eu-repo/semantics/altIdentifier/doi/10.1063/1.2738754
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
application/pdf
dc.publisher.none.fl_str_mv American Institute of Physics
publisher.none.fl_str_mv American Institute of Physics
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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