dc.contributor.author | Konvalinka, Matjaž | |
dc.contributor.author | Pfeiffer, Götz | |
dc.contributor.author | Röver, Claas E. | |
dc.date.accessioned | 2018-09-20T16:13:29Z | |
dc.date.available | 2018-09-20T16:13:29Z | |
dc.date.issued | 2011-01-01 | |
dc.identifier.citation | Konvalinka, Matjaž; Pfeiffer, Götz; Röver, Claas E. (2011). A note on element centralizers in finite coxeter groups. Journal of Group Theory 14 (5), 727-745 | |
dc.identifier.issn | 1433-5883,1435-4446 | |
dc.identifier.uri | http://hdl.handle.net/10379/12303 | |
dc.description.abstract | The normalizer N(W)(W(J)) of a standard parabolic subgroup W(J) of a finite Coxeter group W splits over the parabolic subgroup with complement N(J) consisting of certain minimal length coset representatives of W(J) in W. In this note we show that (with the exception of a small number of cases arising from a situation in Coxeter groups of type D(n)) the centralizer C(W)(w) of an element w epsilon W is in a similar way a semidirect product of the centralizer of w in a suitable small parabolic subgroup W(J) with complement isomorphic to the normalizer complement N(J). Then we use this result to give a new short proof of Solomon's Character Formula and discuss its connection to MacMahon's master theorem. | |
dc.publisher | Walter de Gruyter GmbH | |
dc.relation.ispartof | Journal of Group Theory | |
dc.rights | Attribution-NonCommercial-NoDerivs 3.0 Ireland | |
dc.rights.uri | https://creativecommons.org/licenses/by-nc-nd/3.0/ie/ | |
dc.subject | parabolic subgroups | |
dc.subject | normalizers | |
dc.subject | involutions | |
dc.title | A note on element centralizers in finite coxeter groups | |
dc.type | Article | |
dc.identifier.doi | 10.1515/jgt.2010.074 | |
dc.local.publishedsource | http://arxiv.org/pdf/1005.1186 | |
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