PBW filtration and bases for symplectic Lie algebras

We study the PBW filtration on the highest weight representations $V(\text{la})$ of ${\text{msp}}_{2n}$. This filtration is induced by the standard degree filtration on $U({\text{n}}^{-})$. We give a description of the associated graded $S({\text{n}}^{-})$-module $gr V(\la)$intermsofgeneratorsandrelations\mathrm{.}Wealsoconstructabasisof$gr V(\la)$. As an application we derive a graded combinatorial formula for the character of $V(\text{la})$ and obtain a new class of bases of the modules $V(\text{la})$.