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dc.contributor.authorBishop, Marcus
dc.contributor.authorDouglass, J. Matthew
dc.contributor.authorPfeiffer, Götz
dc.contributor.authorRöhrle, Gerhard
dc.date.accessioned2017-12-05T11:49:06Z
dc.date.available2017-12-05T11:49:06Z
dc.date.issued2012-06-03
dc.identifier.citationBishop, Marcus, Douglass, J. Matthew, Pfeiffer, Götz, & Röhrle, Gerhard. (2013). Computations for Coxeter arrangements and Solomonʼs descent algebra: Groups of rank three and four. Journal of Symbolic Computation, 50(Supplement C), 139-158. doi: https://doi.org/10.1016/j.jsc.2012.06.001en_IE
dc.identifier.issn1095-855X
dc.identifier.urihttp://hdl.handle.net/10379/7009
dc.description.abstractIn recent papers we have refined a conjecture of Lehrer and Solomon expressing the characters of a finite Coxeter group W afforded by the homogeneous components of its Orlik-Solomon algebra as sums of characters induced from linear characters of centralizers of elements of W. Our refined conjecture also relates the Orlik-Solomon characters above to the terms of a decomposition of the regular character of W related to the descent algebra of W. A consequence of our conjecture is that both the regular character of W and the character of the Orlik-Solomon algebra have parallel, graded decompositions as sums of characters induced from linear characters of centralizers of elements of W, one for each conjugacy class of elements of W. The refined conjecture has been proved for symmetric and dihedral groups. In this paper we develop algorithmic tools to prove the conjecture computationally for a given finite Coxeter group. We use these tools to verify the conjecture for all finite Coxeter groups of rank three and four, thus providing previously unknown decompositions of the regular characters and the Orlik-Solomon characters of these groups. (C) 2012 Elsevier B.V. All rights reserved.en_IE
dc.description.sponsorshipWe acknowledge support from the DFG-priority program SPP1489 “Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory”. The third author also wishes to thank Science Foundation Ireland for its support.en_IE
dc.formatapplication/pdfen_IE
dc.language.isoenen_IE
dc.publisherElsevieren_IE
dc.relation.ispartofJournal Of Symbolic Computationen
dc.subjectCoxeter groupen_IE
dc.subjectDescent algebraen_IE
dc.subjectOrlik-Solomon algebraen_IE
dc.subjectPARABOLIC SUBGROUPSen_IE
dc.subjectSPECIAL INVOLUTIONSen_IE
dc.subjectREFLECTION GROUPSen_IE
dc.subjectCENTRALIZERSen_IE
dc.subjectHYPERPLANESen_IE
dc.subjectCOHOMOLOGYen_IE
dc.subjectCOMPLEMENTen_IE
dc.subjectMathematicsen_IE
dc.titleComputations for Coxeter arrangements and Solomon's descent algebra: Groups of rank three and fouren_IE
dc.typeArticleen_IE
dc.date.updated2017-12-04T09:37:51Z
dc.identifier.doi10.1016/j.jsc.2012.06.001
dc.local.publishedsourcehttps://doi.org/10.1016/j.jsc.2012.06.001en_IE
dc.description.peer-reviewedpeer-reviewed
dc.contributor.funder|~|
dc.internal.rssid3130149
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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