Title: Specht Filtrations for Hecke Algebras of Type A
Abstract: Journal of the London Mathematical SocietyVolume 69, Issue 3 p. 623-638 Notes and Papers Specht Filtrations for Hecke Algebras of Type A David J. Hemmer, David J. Hemmer Department of Mathematics, University of Toledo, 2801 W. Bancroft, Toledo, OH 43606, USA, [email protected]Search for more papers by this authorDaniel K. Nakano, Daniel K. Nakano Department of Mathematics, University of Georgia, Athens, GA 30602, USA, [email protected]Search for more papers by this author David J. Hemmer, David J. Hemmer Department of Mathematics, University of Toledo, 2801 W. Bancroft, Toledo, OH 43606, USA, [email protected]Search for more papers by this authorDaniel K. Nakano, Daniel K. Nakano Department of Mathematics, University of Georgia, Athens, GA 30602, USA, [email protected]Search for more papers by this author First published: 23 December 2016 https://doi.org/10.1112/S0024610704005186Citations: 40AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Abstract Let Hq(d) be the Iwahori–Hecke algebra of the symmetric group, where q is a primitive 1th root of unity. Using results from the cohomology of quantum groups and recent results about the Schur functor and adjoint Schur functor, it is proved that, contrary to expectations, for l ⩾ 4 the multiplicities in a Specht or dual Specht module filtration of an Hq(d)-module are well defined. A cohomological criterion is given for when an Hq(d)-module has such a filtration. Finally, these results are used to give a new construction of Young modules that is analogous to the Donkin–Ringel construction of tilting modules. As a corollary, certain decomposition numbers can be equated with extensions between Specht modules. Setting q = 1, results are obtained for the symmetric group in characteristic p ⩾ 5. These results are false in general for p = 2 or 3. Citing Literature Volume69, Issue3June 2004Pages 623-638 RelatedInformation
Publication Year: 2004
Publication Date: 2004-06-01
Language: en
Type: article
Indexed In: ['crossref']
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Cited By Count: 54
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