A Special Class of Rank 10 and 11 Coxeter Groups

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dc.creatorHenneaux, M.
dc.creatorLeston, M.
dc.creatorPersson, D.
dc.creatorSpindel, Ph.
dc.date2006-10-26
dc.date2008-06-26
dc.date.accessioned2026-07-07T11:59:26Z
dc.date.available2026-07-07T11:59:26Z
dc.descriptionIn the course of investigating regular subalgebras of E(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 E(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 infinity. We here go beyond subgroups of the Weyl group of E(10) and classify all rank 10 Coxeter groups 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 E(11).
dc.description20 pages, Typos corrected, Erratum added correcting the total number of rank 11 Coxeter graphs with incidence index 4
dc.identifierhttps://arxiv.org/abs/hep-th/0610278
dc.identifierhttp://arxiv.org/abs/hep-th/0610278
dc.identifierJ.Math.Phys.48:053512,2007; J.Math.Phys.49:099901,2008
dc.identifierdoi:10.1063/1.2738754 10.1063/1.2982250
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/206562
dc.subjectHigh Energy Physics - Theory
dc.subjectGroup Theory
dc.titleA Special Class of Rank 10 and 11 Coxeter Groups
dc.typetext

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