On Koszul duality for Kac-Moody groups
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- by Roman Bezrukavnikov and Zhiwei Yun
- Represent. Theory 17 (2013), 1-98
- DOI: https://doi.org/10.1090/S1088-4165-2013-00421-1
- Published electronically: January 2, 2013
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Abstract:
For any Kac-Moody group $G$ with Borel $B$, we give a monoidal equivalence between the derived category of $B$-equivariant mixed complexes on the flag variety $G/B$ and (a certain completion of) the derived category of $G^\vee$-monodromic mixed complexes on the enhanced flag variety $G^\vee /U^\vee$, here $G^\vee$ is the Langlands dual of $G$. We also prove variants of this equivalence, one of which is the equivalence between the derived category of $U$-equivariant mixed complexes on the partial flag variety $G/P$ and a certain “Whittaker model” category of mixed complexes on $G^\vee /B^\vee$. In all these equivalences, intersection cohomology sheaves correspond to (free-monodromic) tilting sheaves. Our results generalize the Koszul duality patterns for reductive groups in [BGS96].References
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Bibliographic Information
- Roman Bezrukavnikov
- Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
- MR Author ID: 347192
- Email: bezrukav@math.mit.edu
- Zhiwei Yun
- Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
- Address at time of publication: Department of Mathematics, Stanford University, 450 Serra Mall, Stanford, California 94305
- MR Author ID: 862829
- Email: zyun@stanford.edu
- Received by editor(s): January 15, 2011
- Received by editor(s) in revised form: July 7, 2011, August 13, 2011, and April 11, 2012
- Published electronically: January 2, 2013
- Additional Notes: The first author was partly supported by the NSF grant DMS-0854764.
The second author was supported by the NSF grant DMS-0635607 and Zurich Financial Services as a member at the Institute for Advanced Study, and by the NSF grant DMS-0969470. - © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Represent. Theory 17 (2013), 1-98
- MSC (2010): Primary 20G44, 14M15, 14F05
- DOI: https://doi.org/10.1090/S1088-4165-2013-00421-1
- MathSciNet review: 3003920