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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.


D-modules on the affine flag variety and representations of affine Kac-Moody algebras
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by Edward Frenkel and Dennis Gaitsgory
Represent. Theory 13 (2009), 470-608
Published electronically: November 2, 2009


The present paper studies the connection between the category of modules over the affine Kac-Moody Lie algebra at the critical level, and the category of D-modules on the affine flag scheme $G((t))/I$, where $I$ is the Iwahori subgroup. We prove a localization-type result, which establishes an equivalence between certain subcategories on both sides. We also establish an equivalence between a certain subcategory of Kac-Moody modules, and the category of quasi-coherent sheaves on the scheme of Miura opers for the Langlands dual group, thereby proving a conjecture of the authors in 2006.
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Bibliographic Information
  • Edward Frenkel
  • Affiliation: Department of Mathematics, University of California, Berkeley, California 94720
  • MR Author ID: 257624
  • ORCID: 0000-0001-6519-8132
  • Email:
  • Dennis Gaitsgory
  • Affiliation: Department of Mathematics, Harvard University, Cambridge, Massachusetts 02138
  • Email:
  • Received by editor(s): December 6, 2007
  • Received by editor(s) in revised form: July 6, 2009
  • Published electronically: November 2, 2009
  • Additional Notes: The first author was supported by DARPA and AFOSR through the grant FA9550-07-1-0543.
    The second author was supported by NSF grant 0600903.
  • © Copyright 2009 Edward Frenkel and Dennis Gaitsgory
  • Journal: Represent. Theory 13 (2009), 470-608
  • MSC (2010): Primary 17B67; Secondary 13N10
  • DOI:
  • MathSciNet review: 2558786