PBW filtration and bases for irreducible modules in type A_n

Feigin, E., Fourier, G. and Littelmann, P. (2011) PBW filtration and bases for irreducible modules in type A_n. Transformation Groups, 16(1), pp. 71-89. (doi: 10.1007/s00031-010-9115-4)

Abstract

We study the PBW filtration on the highest weight representations V(λ) of sl n+1 . This filtration is induced by the standard degree filtration on U(n −) . We give a description of the associated graded S(n −) -module gr V(λ) in terms of generators and relations. We also construct a basis of gr V(λ). As an application we derive a graded combinatorial character formula for V(λ), and we obtain a new class of bases of the modules V(λ) conjectured by Vinberg in 2005.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Fourier, Dr Ghislain
• Authors: Feigin, E., Fourier, G., and Littelmann, P.
• Subjects: Q Science > QA Mathematics
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Transformation Groups
• ISSN: 1083-4362
• ISSN (Online): 1531-586X