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Representation Theory

Published by the American Mathematical Society, the Representation Theory (ERT) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.7.

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The PBW filtration
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by Evgeny Feigin PDF
Represent. Theory 13 (2009), 165-181 Request permission


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.
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Additional 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:
  • 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:
  • MathSciNet review: 2506263