2000 character limit reached
PBW filtration and bases for symplectic Lie algebras (1010.2321v1)
Published 12 Oct 2010 in math.RT and math.CO
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 $V(\la)$.