## 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 - DOI: https://doi.org/10.1090/S1088-4165-09-00360-4
- Published electronically: November 2, 2009

## Abstract:

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.## References

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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: frenkel@math.berkeley.edu
**Dennis Gaitsgory**- Affiliation: Department of Mathematics, Harvard University, Cambridge, Massachusetts 02138
- Email: gaitsgde@math.harvard.edu
- 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: https://doi.org/10.1090/S1088-4165-09-00360-4
- MathSciNet review: 2558786