PBW filtration and bases for irreducible modules in type An

Evgeny Feigin, Ghislain Fourier, Peter Littelmann

Research output: Contribution to journalArticlepeer-review

68 Citations (Scopus)

Abstract

We study the PBW filtration on the highest weight representations V(λ) of SLn+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.

Original languageEnglish
Pages (from-to)71-89
Number of pages19
JournalTransformation Groups
Volume16
Issue number1
DOIs
Publication statusPublished - Mar 2011
Externally publishedYes

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