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Representation Theory

Published by the American Mathematical Society since 1997, this electronic-only journal is devoted to research in representation theory and seeks to maintain a high standard for exposition as well as for mathematical content. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.71.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


The PBW filtration
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by Evgeny Feigin
Represent. Theory 13 (2009), 165-181
Published electronically: May 1, 2009


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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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:
  • 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