PBW Filtration and Bases for Symplectic Lie Algebras

DOI10.1093/IMRN/RNR014zbMATH Open1233.17007arXiv1010.2321OpenAlexW2962768461MaRDI QIDQ3108563

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Publication date: 4 January 2012

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Abstract: We study the PBW filtration on the highest weight representations $V(la)$ of $ms{p}_{2n}$. This filtration is induced by the standard degree filtration on $U{(}^{-})$. We give a description of the associated graded $S{(}^{-})$-module $grV(la)$ in terms of generators and relations. We also construct a basis of $grV(la)$. 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 $V(la)$.

Full work available at URL: https://arxiv.org/abs/1010.2321

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