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D-modules on the affine flag variety and representations of affine Kac-Moody algebras
Author(s):
Edward
Frenkel;
Dennis
Gaitsgory
Journal:
Represent. Theory
13
(2009),
470-608.
MSC (2010):
Primary 17B67;
Secondary 13N10
Posted:
November 2, 2009
MathSciNet review:
2558786
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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  , where  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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Additional Information:
Edward
Frenkel
Affiliation:
Department of Mathematics, University of California, Berkeley, California 94720
Email:
frenkel@math.berkeley.edu
Dennis
Gaitsgory
Affiliation:
Department of Mathematics, Harvard University, Cambridge, Massachusetts 02138
Email:
gaitsgde@math.harvard.edu
DOI:
10.1090/S1088-4165-09-00360-4
PII:
S 1088-4165(09)00360-4
Received by editor(s):
December 6, 2007
Received by editor(s) in revised form:
July 6, 2009
Posted:
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 of article:
Copyright
2009,
Edward Frenkel and Dennis Gaitsgory
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