PBW filtration and bases for irreducible modules in type A_n

We study the PBW filtration on the highest weight representations V(λ) of sl n+1 . This filtration is induced by the standard degree filtration on U(n −) . We give a description of the associated graded S(n −) -module gr V(λ) in terms of generators and relations. We also construct a basis of gr V(λ). As an application we derive a graded combinatorial character formula for V(λ), and we obtain a new class of bases of the modules V(λ) conjectured by Vinberg in 2005