Categorification of Wedderburn's basis for C[S-n]
2008 (English)In: Archiv der Mathematik, ISSN 0003-889X, Vol. 91, no 1, 1-11 p.Article in journal (Refereed) Published
M. Neunhoffer studies in  a certain basis of C[S-n] with the origins in  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 () 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.
categorification, simple modules, projective module, projective functor, annihilator, Lie algebra, universal enveloping algebra, Kahdan-Lusztig basis
IdentifiersURN: urn:nbn:se:uu:diva-105797DOI: 10.1007/s00013-008-2571-6ISI: 000257486000001OAI: oai:DiVA.org:uu-105797DiVA: diva2:222500