## The PBW filtration

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- by Evgeny Feigin
- Represent. Theory
**13**(2009), 165-181 - DOI: https://doi.org/10.1090/S1088-4165-09-00349-5
- Published electronically: May 1, 2009
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## Abstract:

In this paper we study the PBW filtration on irreducible integrable highest weight representations of affine Kac-Moody algebras $\widehat {\mathfrak {g}}$. The $n$-th space of this filtration is spanned by the vectors $x_1\dots x_s v$, where $x_i\in \widehat {\mathfrak {g}}$, $s\le n$, 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 $\mathfrak {g}$ of the type $A_1$ we prove our conjecture and derive the fermionic formula for the graded character.## References

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## Bibliographic Information

**Evgeny Feigin**- Affiliation: Tamm Theory Division, Lebedev Physics Institute, Russian Academy of Sciences, Russia, 119991, Moscow, Leninski prospect, 53 – and –
*Independent University of Moscow, Russia, Moscow, 119002, Bol’shoi Vlas’evskii, 11* - Email: evgfeig@gmail.com
- Received by editor(s): November 15, 2007
- Received by editor(s) in revised form: February 4, 2009
- Published electronically: May 1, 2009
- © Copyright 2009
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Represent. Theory
**13**(2009), 165-181 - MSC (2000): Primary 17B67, 81R10
- DOI: https://doi.org/10.1090/S1088-4165-09-00349-5
- MathSciNet review: 2506263