PBW filtration and bases for symplectic Lie algebras

By Evgeny Feigin, Ghislain Fourier, P. Littelmann. 2010

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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 $V(\la)$.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/95625b33dcc7dd53424bb5c12aa3927769197a5f