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Статья

PBW filtration and bases for symplectic Lie algebras

International Mathematics Research Notices. 2011. Vol. 2011. No. 24. P. 5760-5784.
Feigin E., Fourier G., Littelmann P.
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 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 formula for the character of V(λ) and obtain a new class of bases of the modules V(λ).