PBW filtration and bases for irreducible modules in type A_n

2010/02/28 by Evgeny Feigin, Ghislain Fourier, Peter Littelmann · 3 citations
Mathematics · #math.RT #math.CO #msc:17B10 #msc:05E10

paper · pdf

published as Transform. Groups 165 (2011), no. 1, 71-89 · 18 pages, references added

arxiv created 2010/04/11 · arxiv updated 2012/12/18

Abstract

We study the PBW filtration on the highest weight representations V(\la) of \msl_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(\la) in terms of generators and relations. We also construct a basis of gr V(\la). As an application we derive a graded combinatorial character formula for V(\la), and we obtain a new class of bases of the modules V(\la) conjectured by Vinberg in 2005.

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