Pbw-filtration over z and compatible bases for vℤ(λ) in type an and cn

Abstract

We study the PBW-filtration on the highest weight representations V (λ) of the Lie algebras of type An and Cn. This filtration is induced by the standard degree filtration on U(n-). 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. © Springer-Verlag London 2013.