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dc.contributor.authorBishop, Marcus
dc.contributor.authorDouglass, J. Matthew
dc.contributor.authorPfeiffer, Götz
dc.contributor.authorRöhrle, Gerhard
dc.date.accessioned2017-12-04T16:18:58Z
dc.date.available2017-12-04T16:18:58Z
dc.date.issued2013-01-08
dc.identifier.citationBishop, Marcus, Douglass, J. Matthew, Pfeiffer, Götz, & Röhrle, Gerhard. (2013). Computations for Coxeter arrangements and Solomonʼs descent algebra II: Groups of rank five and six. Journal of Algebra, 377(Supplement C), 320-332. doi: https://doi.org/10.1016/j.jalgebra.2012.11.047en_IE
dc.identifier.issn0021-8693
dc.identifier.urihttp://hdl.handle.net/10379/7004
dc.description.abstractIn recent papers we have refined a conjecture of Lehrer and Solomon expressing the character of a finite Coxeter group W acting on the graded components of its Orlik-Solomon algebra as a sum of characters induced from linear characters of centralizers of elements of W. The refined conjecture relates the character above to a decomposition of the regular character of W related to Solomon's descent algebra of W. The refined conjecture has been proved for symmetric and dihedral groups, as well as for finite Coxeter groups of rank three and four. In this paper, we prove the conjecture for finite Coxeter groups of rank five and six. The techniques developed and implemented in this paper provide previously unknown decompositions of the regular and Orlik-Solomon characters of the groups considered. (C) 2012 Elsevier Inc. All rights reserved.en_IE
dc.description.sponsorshipThe authors would like to acknowledge support from the DFG-priority program SPP1489 “Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory”.en_IE
dc.formatapplication/pdfen_IE
dc.language.isoenen_IE
dc.publisherElsevieren_IE
dc.relation.ispartofJournal Of Algebraen
dc.subjectCoxeter groupen_IE
dc.subjectDescent algebraen_IE
dc.subjectOrlik-Solomon algebraen_IE
dc.subjectREFLECTION GROUPSen_IE
dc.subjectMathematicsen_IE
dc.titleComputations for Coxeter arrangements and Solomon's descent algebra II: Groups of rank five and sixen_IE
dc.typeArticleen_IE
dc.date.updated2017-12-04T12:11:26Z
dc.identifier.doi10.1016/j.jalgebra.2012.11.047
dc.local.publishedsourcehttps://doi.org/10.1016/j.jalgebra.2012.11.047en_IE
dc.description.peer-reviewedpeer-reviewed
dc.contributor.funder|~|
dc.internal.rssid4341217
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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