A special class of rank 10 and 11 Coxeter groups

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 (M. Henneaux, e-print hep-th/0606123). These Coxeter g...

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Publicado: 2007
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00222488_v48_n5_p_Henneaux
http://hdl.handle.net/20.500.12110/paper_00222488_v48_n5_p_Henneaux
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_00222488_v48_n5_p_Henneaux
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spelling paper:paper_00222488_v48_n5_p_Henneaux2023-06-08T14:48:14Z A special class of rank 10 and 11 Coxeter groups 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 (M. Henneaux, e-print 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 groups with these properties. We find 21 distinct Coxeter groups of which 7 were already described by M. Henneaux, (e-print 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). © 2007 American Institute of Physics. 2007 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00222488_v48_n5_p_Henneaux http://hdl.handle.net/20.500.12110/paper_00222488_v48_n5_p_Henneaux
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
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 (M. Henneaux, e-print 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 groups with these properties. We find 21 distinct Coxeter groups of which 7 were already described by M. Henneaux, (e-print 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). © 2007 American Institute of Physics.
title A special class of rank 10 and 11 Coxeter groups
spellingShingle A special class of rank 10 and 11 Coxeter groups
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 special class of rank 10 and 11 coxeter groups
publishDate 2007
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00222488_v48_n5_p_Henneaux
http://hdl.handle.net/20.500.12110/paper_00222488_v48_n5_p_Henneaux
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