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arXiv · 1204.1854

PBW--filtration over $\bz$ and compatible bases for $V_\bz(\la)$ in type ${\tt A}_n$ and ${\tt C}_n$

Evgeny Feigin·Ghislain Fourier·Peter Littelmann
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Abstract

We study the PBW-filtration on the highest weight representations $V(\la)$ of the Lie algebras of type ${\tt A}_{n}$ and ${\tt C}_{n}$. This filtration is induced by the standard degree filtration on $\U(\fn^-)$. In previous papers, the authors studied the filtration and the associated graded algebras and modules over the complex numbers. The aim of this paper is to present a proof of the results which holds over the integers and hence makes the whole construction available over any field.

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Evgeny Feigin, Ghislain Fourier, Peter Littelmann. 2012-04-09. PBW--filtration over $\bz$ and compatible bases for $V_\bz(\la)$ in type ${\tt A}_n$ and ${\tt C}_n$. https://arxiv.org/abs/1204.1854

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