PBW filtration and bases for symplectic lie algebras

Evgeny Feigin*, Ghislain Fourier, Peter Littelmann

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

50 Scopus citations

Abstract

We study the PBW filtration on the highest weight representations V (λ) of sp2n. This filtration is induced by the standard degree filtration on U(n-). We give a description of the associated graded S(n-)-module grV(λ) in terms of generators and relations. We also construct a basis of grV(λ). As an application we derive a graded combinatorial formula for the character of V(λ) and obtain a new class of bases of the modules V(λ).

Original languageEnglish
Pages (from-to)5760-5784
Number of pages25
JournalInternational Mathematics Research Notices
Volume2011
Issue number24
DOIs
StatePublished - 1 Jan 2011
Externally publishedYes

Funding

FundersFunder number
Deutsche Forschungsgemeinschaft
Russian Foundation for Basic Research09-01-00058, NSh-3472.2008.2

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