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Categorification of Wedderburn's basis for C[S-n]
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra, Geometry and Logic. (Algebra)
2008 (English)In: Archiv der Mathematik, ISSN 0003-889X, Vol. 91, no 1, 1-11 p.Article in journal (Refereed) Published
Abstract [en]

M. Neunhoffer studies in [21] a certain basis of C[S-n] with the origins in [14] and shows that this basis is in fact Wedderburn's basis, hence decomposes the right regular representation of S-n into a direct sum of irreducible representations (i.e. Specht or cell modules). In the present paper we rediscover essentially the same basis with a categorical origin coming from projective-injective modules in certain subcategories of the BGG-category O. Inside each of these categories, there is a dominant projective module which plays a crucial role in our arguments and will additionally be used to show that Kostant's problem ([10]) has a negative answer for some simple highest weight module over the Lie algebra sl(4). This disproves the general belief that Kostant's problem should have a positive answer for all simple highest weight modules in type A.

Place, publisher, year, edition, pages
2008. Vol. 91, no 1, 1-11 p.
Keyword [en]
categorification, simple modules, projective module, projective functor, annihilator, Lie algebra, universal enveloping algebra, Kahdan-Lusztig basis
National Category
Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-105797DOI: 10.1007/s00013-008-2571-6ISI: 000257486000001OAI: oai:DiVA.org:uu-105797DiVA: diva2:222500
Available from: 2009-06-08 Created: 2009-06-08 Last updated: 2009-10-29Bibliographically approved

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