Categorification of Wedderburn’s basis for C[S-n]

Mazorchuk, V. and Stroppel, C. (2008) Categorification of Wedderburn’s basis for C[S-n]. Archiv der Mathematik, 91(1), pp. 1-11. (doi: 10.1007/s00013-008-2571-6)

Abstract

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.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Stroppel, Dr Catharina
• Authors: Mazorchuk, V., and Stroppel, C.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Archiv der Mathematik
• ISSN: 0003-889X