PBW filtration and bases for symplectic Lie algebras

2010/10/12 by Evgeny Feigin, Ghislain Fourier, Peter Littelmann · 1 citation
Mathematics · #math.RT #math.CO

paper · pdf

published as Int. Math. Res. Not. IMRN 2011, no. 24, 5760-5784 · 21 pages

arxiv created 2010/10/12 · arxiv updated 2012/12/18

Abstract

We study the PBW filtration on the highest weight representations V(\la) of \msp_2n. 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 formula for the character of V(\la) and obtain a new class of bases of the modules V(\la).

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