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Cuspidal sl(n)-modules and deformations of certain Brauer tree algebras
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra, Geometry and Logic.
2011 (English)In: Advances in Mathematics, ISSN 0001-8708, E-ISSN 1090-2082, Vol. 228, no 2, 1008-1042 p.Article in journal (Refereed) Published
Abstract [en]

We show that the algebras describing blocks of the category of cuspidal weight (resp. generalized weight) sl(n) -modules are one-parameter (resp. multi-parameter) deformations of certain Brauer tree algebras. We explicitly determine these deformations both graded and ungraded. The algebras we deform also appear as special centralizer subalgebras of Temperley-Lieb algebras or as generalized Khovanov algebras. They show up in the context of highest weight representations of the Virasoro algebra, in the context of rational representations of the general linear group and Schur algebras and in the study of the Milnor fiber of Kleinian singularities.

Place, publisher, year, edition, pages
2011. Vol. 228, no 2, 1008-1042 p.
Keyword [en]
Weight module, Cuspidal module, Lie algebra, Associative algebra, Deformation
National Category
URN: urn:nbn:se:uu:diva-158856DOI: 10.1016/j.aim.2011.06.005ISI: 000293667800009OAI: oai:DiVA.org:uu-158856DiVA: diva2:442256
Available from: 2011-09-20 Created: 2011-09-19 Last updated: 2012-02-16Bibliographically approved

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Algebra, Geometry and Logic
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