dc.contributor.author | Bishop, Marcus | |
dc.contributor.author | Douglass, J. Matthew | |
dc.contributor.author | Pfeiffer, Götz | |
dc.contributor.author | Röhrle, Gerhard | |
dc.date.accessioned | 2017-12-05T11:49:06Z | |
dc.date.available | 2017-12-05T11:49:06Z | |
dc.date.issued | 2012-06-03 | |
dc.identifier.citation | Bishop, 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.2012.06.001 | en_IE |
dc.identifier.issn | 1095-855X | |
dc.identifier.uri | http://hdl.handle.net/10379/7009 | |
dc.description.abstract | In 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.sponsorship | We 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.format | application/pdf | en_IE |
dc.language.iso | en | en_IE |
dc.publisher | Elsevier | en_IE |
dc.relation.ispartof | Journal Of Symbolic Computation | en |
dc.rights | Attribution-NonCommercial-NoDerivs 3.0 Ireland | |
dc.rights.uri | https://creativecommons.org/licenses/by-nc-nd/3.0/ie/ | |
dc.subject | Coxeter group | en_IE |
dc.subject | Descent algebra | en_IE |
dc.subject | Orlik-Solomon algebra | en_IE |
dc.subject | PARABOLIC SUBGROUPS | en_IE |
dc.subject | SPECIAL INVOLUTIONS | en_IE |
dc.subject | REFLECTION GROUPS | en_IE |
dc.subject | CENTRALIZERS | en_IE |
dc.subject | HYPERPLANES | en_IE |
dc.subject | COHOMOLOGY | en_IE |
dc.subject | COMPLEMENT | en_IE |
dc.subject | Mathematics | en_IE |
dc.title | Computations for Coxeter arrangements and Solomon's descent algebra: Groups of rank three and four | en_IE |
dc.type | Article | en_IE |
dc.date.updated | 2017-12-04T09:37:51Z | |
dc.identifier.doi | 10.1016/j.jsc.2012.06.001 | |
dc.local.publishedsource | https://doi.org/10.1016/j.jsc.2012.06.001 | en_IE |
dc.description.peer-reviewed | peer-reviewed | |
dc.contributor.funder | |~| | |
dc.internal.rssid | 3130149 | |
dc.local.contact | Gotz Pfeiffer, Dept. Of Mathematics, Room C208, Áras De Brún, Nui Galway. 3591 Email: goetz.pfeiffer@nuigalway.ie | |
dc.local.copyrightchecked | Yes | |
dc.local.version | ACCEPTED | |
nui.item.downloads | 1073 | |