Show simple item record

dc.contributor.authorFriedl, Tobias
dc.contributor.authorRiener, Cordian
dc.contributor.authorSanyal, Raman
dc.date.accessioned2019-03-19T22:49:47Z
dc.date.available2019-03-19T22:49:47Z
dc.date.issued2017-10-18
dc.description.abstractLet <i>X</i> be a nonempty real variety that is invariant under the action of a reflection group <i>G</i>. We conjecture that if <i>X</i> is defined in terms of the first <i>k</i> basic invariants of <i>G</i> (ordered by degree), then <i>X</i> meets a <i>k</i>-dimensional flat of the associated reflection arrangement. We prove this conjecture for the infinite types, reflection groups of rank at most <i>3</i>, and <i>F<sub>4</sub></i> and we give computational evidence for <i>H<sub>4</sub></i>. This is a generalization of Timofte's degree principle to reflection groups. For general reflection groups, we compute nontrivial upper bounds on the minimal dimension of flats of the reflection arrangement meeting <i>X</i> from the combinatorics of parabolic subgroups. We also give generalizations to real varieties invariant under Lie groups.en_US
dc.description.sponsorshipDFG-Collaborative Research Center Dahlem Research School at the Freie Universität Berlin.en_US
dc.descriptionSource at <a href=https://doi.org/10.1090/proc/13821>https://doi.org/10.1090/proc/13821</a>.en_US
dc.identifier.citationFriedl, T., Riener, C. & Sanyal, R. (2018). Reflection groups, arrangements, and invariant real varieties. <i>Proceedings of the American Mathematical Society, 146</i>(3), 1031-1045. https://doi.org/10.1090/proc/13821en_US
dc.identifier.cristinIDFRIDAID 1573461
dc.identifier.doi10.1090/proc/13821
dc.identifier.issn0002-9939
dc.identifier.issn1088-6826
dc.identifier.urihttps://hdl.handle.net/10037/15030
dc.language.isoengen_US
dc.publisherAmerican Mathematical Societyen_US
dc.relation.journalProceedings of the American Mathematical Society
dc.rights.accessRightsopenAccessen_US
dc.subjectreflection groupsen_US
dc.subjectreflection arrangementsen_US
dc.subjectinvariant real varietiesen_US
dc.subjectreal orbit spacesen_US
dc.subjectVDP::Mathematics and natural science: 400::Mathematics: 410::Algebra/algebraic analysis: 414en_US
dc.subjectVDP::Matematikk og Naturvitenskap: 400::Matematikk: 410::Algebra/algebraisk analyse: 414en_US
dc.titleReflection groups, arrangements, and invariant real varietiesen_US
dc.typeJournal articleen_US
dc.typeTidsskriftartikkelen_US
dc.typePeer revieweden_US


File(s) in this item

Thumbnail

This item appears in the following collection(s)

Show simple item record