PBW filtration and bases for irreducible modules in type \({\text{\textsf{A}}}_{n}\)

DOI10.1007/S00031-010-9115-4zbMATH Open1237.17011arXiv1002.0674OpenAlexW2166544109MaRDI QIDQ537725

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Publication date: 23 May 2011

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Abstract: We study the PBW filtration on the highest weight representations $V(la)$ of $ms{l}_{n+1}$. 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 character formula for $V(la)$, and we obtain a new class of bases of the modules $V(la)$ conjectured by Vinberg in 2005.

Full work available at URL: https://arxiv.org/abs/1002.0674

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