PBW--filtration over \bz and compatible bases for V_\bz(\la) in type \tt A_n and \tt C_n

2012/04/09 by Evgeny Feigin, Feigin, Evgeny, Ghislain Fourier +3
Mathematics · #17B10 #FOS: Mathematics #Representation Theory (math.RT) #math.RT #msc:17B10

paper · pdf · doi:10.48550/arxiv.1204.1854

arxiv created 2012/04/09 · arxiv updated 2012/04/10

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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