The PBW filtration

Evgeny Feigin

doi:10.1090/S1088-4165-09-00349-5

The PBW filtration

Evgeny Feigin^*

^*Corresponding author for this work

RAS - P.N. Lebedev Physics Institute
Independent University of Moscow

Research output: Contribution to journal › Article › peer-review

28 Scopus citations

Abstract

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 language	English
Pages (from-to)	165-181
Number of pages	17
Journal	Representation Theory
Volume	13
Issue number	9
DOIs	https://doi.org/10.1090/S1088-4165-09-00349-5
State	Published - 1 May 2009
Externally published	Yes

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The PBW filtration

Abstract

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