The PBW filtration

Evgeny Feigin*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


In this paper we study the PBW filtration on irreducible integrable highest weight representations of affine Kac-Moody algebras ĝ. The n-th space of this filtration is spanned by the vectors x1. xsv, where xi ∈ ĝ, s ≤ n, and v is a highest weight vector. For the vacuum module we give a conjectural description of the corresponding adjoint graded space in terms of generators and relations. For g of the type A1 we prove our conjecture and derive the fermionic formula for the graded character.

Original languageEnglish
Pages (from-to)165-181
Number of pages17
JournalRepresentation Theory
Issue number9
StatePublished - 1 May 2009
Externally publishedYes


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