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- W2952115795 abstract "M. Neunh{o}ffer studies in cite{Ne} a certain basis of $mathbb{C}[S_n]$ with the origins in cite{Lu} and shows that this basis is in fact Wedderburn's basis. In particular, in this basis the right regular representation of $S_n$ decomposes 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 $mathcal{O}$. An important role in our arguments is played by the dominant projective module in each of these categories. As a biproduct of the study of this dominant projective module we show that {it Kostant's problem} (cite{Jo}) has a negative answer for some simple highest weight module over the Lie algebra $mathfrak{sl}_4$, which disproves the general belief that Kostant's problem should have a positive answer for all simple highest weight modules in type $A$." @default.
- W2952115795 created "2019-06-27" @default.
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- W2952115795 date "2007-08-29" @default.
- W2952115795 modified "2023-09-27" @default.
- W2952115795 title "Categorification of Wedderburn's basis for mathbb{C}[S_n]" @default.
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