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dc.contributor.authorDouglass, J. Matthew
dc.contributor.authorPfeiffer, Götz
dc.contributor.authorRöhrle, Gerhard
dc.date.accessioned2017-12-05T10:29:03Z
dc.date.available2017-12-05T10:29:03Z
dc.date.issued2014-06-19
dc.identifier.citationDouglass, JM,Pfeiffer, G,Rohrle, G (2014) 'COHOMOLOGY OF COXETER ARRANGEMENTS AND SOLOMON'S DESCENT ALGEBRA'. Transactions Of The American Mathematical Society, 366 :5379-5407, doi:10.1090/S0002-9947-2014-06060-1en_IE
dc.identifier.issn1088-6850
dc.identifier.urihttp://hdl.handle.net/10379/7007
dc.description.abstractWe refine a conjecture by Lehrer and Solomon on the structure of the Orlik-Solomon algebra of a finite Coxeter group W and relate it to the descent algebra of W. As a result, we claim that both the group algebra of W and the Orlik-Solomon algebra of W can be decomposed into a sum of induced one-dimensional representations of element centralizers, one for each conjugacy class of elements of W. We give a uniform proof of the claim for symmetric groups. In addition, we prove that a relative version of the conjecture holds for every pair (W, W-L), where W is arbitrary and W-L is a parabolic subgroup of W, all of whose irreducible factors are of type A.en_IE
dc.description.sponsorshipThe authors would like to acknowledge support from 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. The second author wishes to acknowledge support from Science Foundation Ireland.en_IE
dc.language.isoenen_IE
dc.publisherAmerican Mathematical Societyen_IE
dc.relation.ispartofTransactions Of The American Mathematical Societyen
dc.rightsAttribution-NonCommercial-NoDerivs 3.0 Ireland
dc.rights.urihttps://creativecommons.org/licenses/by-nc-nd/3.0/ie/
dc.subjectHOCHSCHILD HOMOLOGYen_IE
dc.subjectHYPERPLANESen_IE
dc.subjectDECOMPOSITIONen_IE
dc.subjectCOMPUTATIONSen_IE
dc.subjectCENTRALIZERSen_IE
dc.subjectCOMPLEMENTSen_IE
dc.subjectRINGen_IE
dc.subjectAlgebraen_IE
dc.subjectMathematicsen_IE
dc.titleCohomology of Coxeter arrangements and Solomon's descent algebraen_IE
dc.typeArticleen_IE
dc.date.updated2017-12-04T09:34:21Z
dc.identifier.doi10.1090/S0002-9947-2014-06060-1
dc.local.publishedsourcehttps://doi.org/10.1090/S0002-9947-2014-06060-1en_IE
dc.description.peer-reviewedpeer-reviewed
dc.contributor.funder|~|
dc.internal.rssid8025496
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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Attribution-NonCommercial-NoDerivs 3.0 Ireland
Except where otherwise noted, this item's license is described as Attribution-NonCommercial-NoDerivs 3.0 Ireland