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dc.contributor.authorDolan, J. Matthew
dc.contributor.authorPfeiffer, Götz
dc.contributor.authorRöhrle, Gerhard
dc.date.accessioned2017-12-05T14:35:13Z
dc.date.available2017-12-05T14:35:13Z
dc.date.issued2012-07-20
dc.identifier.citationDouglass, J. Matthew, Pfeiffer, Götz, & Röhrle, Gerhard. (2012). An inductive approach to Coxeter arrangements and Solomon’s descent algebra. Journal of Algebraic Combinatorics, 35(2), 215-235. doi: 10.1007/s10801-011-0301-9en_IE
dc.identifier.issn1572-9192
dc.identifier.urihttp://hdl.handle.net/10379/7013
dc.description.abstractIn our recent paper (Douglass et al. arXiv: 1101.2075 (2011)), we claimed that both the group algebra of a finite Coxeter group W as well as the Orlik-Solomon algebra of W can be decomposed into a sum of induced one-dimensional representations of centralizers, one for each conjugacy class of elements of W, and gave a uniform proof of this claim for symmetric groups. In this note, we outline an inductive approach to our conjecture. As an application of this method, we prove the inductive version of the conjecture for finite Coxeter groups of rank up to 2.en_IE
dc.description.sponsorshipThe authors acknowledge the financial support of the DFG-priority programme SPP1489 “Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory”. Part of the research for this paper was carried out while the authors were staying at the Mathematical Research Institute Oberwolfach supported by the “Research in Pairs” programme in 2010. The second author wishes to acknowledge support from Science Foundation Ireland.en_IE
dc.formatapplication/pdfen_IE
dc.language.isoenen_IE
dc.publisherSpringer Verlagen_IE
dc.relation.ispartofJournal Of Algebraic Combinatoricsen
dc.subjectCoxeter groupsen_IE
dc.subjectReflection arrangementsen_IE
dc.subjectDescent algebraen_IE
dc.subjectDihedral groupsen_IE
dc.subjectPARABOLIC SUBGROUPSen_IE
dc.subjectMathematicsen_IE
dc.titleAn inductive approach to Coxeter arrangements and Solomon's descent algebraen_IE
dc.typeArticleen_IE
dc.date.updated2017-12-04T14:02:35Z
dc.identifier.doi10.1007/s10801-011-0301-9
dc.local.publishedsourcehttp://dx.doi.org/10.1007/s10801-011-0301-9en_IE
dc.description.peer-reviewedpeer-reviewed
dc.contributor.funder|~|
dc.internal.rssid2196327
dc.local.contactGotz Pfeiffer, Dept. Of Mathematics, Room C208, Áras De Brún, Nui Galway. 3591 Email: goetz.pfeiffer@nuigalway.ie
dc.local.copyrightcheckedYes
dc.local.versionACCEPTED
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