[1506.03332] Absolute order in general linear groups - arXiv

Abstract: This paper studies a partial order on the general linear group GL(V) called the absolute order, derived from viewing GL(V) as a ... GivingWeek! ShowyoursupportforOpenSciencebydonatingtoarXivduringGivingWeek,April25th-29th. DONATE Mathematics>Combinatorics arXiv:1506.03332(math) [Submittedon10Jun2015(v1),lastrevised29Jun2015(thisversion,v2)] Title:Absoluteorderingenerallineargroups Authors:JiaHuang,JoelBrewsterLewis,VictorReiner DownloadPDF Abstract:ThispaperstudiesapartialorderonthegenerallineargroupGL(V)called theabsoluteorder,derivedfromviewingGL(V)asagroupgeneratedby reflections,thatis,elementswhosefixedspacehascodimensionone.The absoluteorderonGL(V)isshowntohavetwoequivalentdescriptions,onevia additivityoflengthforfactorizationsintoreflections,theothervia additivityoffixedspacecodimensions.Othergeneralpropertiesoftheorder arederived,includingself-dualityofitsintervals. WorkingoverafinitefieldF_q,itisshownviaacomplexcharacter computationthattheposetintervalfromtheidentitytoaSingercycle(orany regularellipticelement)inGL_n(F_q)hasastrikinglysimpleformulaforthe numberofchainspassingthroughaprescribedsetofranks. Comments: 26pages.v2:Minoredits;Question6.3andsomereferencesadded Subjects: Combinatorics(math.CO);RepresentationTheory(math.RT) MSCclasses: 20G40,05E10,20C33 Citeas: arXiv:1506.03332[math.CO]   (or arXiv:1506.03332v2[math.CO]forthisversion) Journal reference: J.Lond.Math.Soc.(2)95(2017),no.1,223--247 RelatedDOI: https://doi.org/10.1112/jlms.12013 Focustolearnmore DOI(s)linkingtorelatedresources SubmissionhistoryFrom:JoelLewis[viewemail] [v1] Wed,10Jun201514:47:13UTC(30KB)[v2] Mon,29Jun201521:02:37UTC(30KB) Full-textlinks: Download: PDF PostScript Otherformats (license) Currentbrowsecontext:math.CO new | recent | 1506 Changetobrowseby: math math.RT References&Citations NASAADSGoogleScholar SemanticScholar a exportbibtexcitation Loading... Bibtexformattedcitation × loading... Dataprovidedby: Bookmark BibliographicTools BibliographicandCitationTools BibliographicExplorerToggle BibliographicExplorer(WhatistheExplorer?) LitmapsToggle Litmaps(WhatisLitmaps?) scite.aiToggle sciteSmartCitations(WhatareSmartCitations?) Code&Data CodeandDataAssociatedwiththisArticle arXivLinkstoCodeToggle arXivLinkstoCode&Data(WhatisLinkstoCode&Data?) Demos Demos ReplicateToggle Replicate(WhatisReplicate?) RelatedPapers RecommendersandSearchTools ConnectedPapersToggle ConnectedPapers(WhatisConnectedPapers?) Corerecommendertoggle CORERecommender(WhatisCORE?) AboutarXivLabs arXivLabs:experimentalprojectswithcommunitycollaborators arXivLabsisaframeworkthatallowscollaboratorstodevelopandsharenewarXivfeaturesdirectlyonourwebsite. BothindividualsandorganizationsthatworkwitharXivLabshaveembracedandacceptedourvaluesofopenness,community,excellence,anduserdataprivacy.arXiviscommittedtothesevaluesandonlyworkswithpartnersthatadheretothem. HaveanideaforaprojectthatwilladdvalueforarXiv'scommunity?LearnmoreaboutarXivLabsandhowtogetinvolved. Whichauthorsofthispaperareendorsers?| DisableMathJax(WhatisMathJax?)