On Koszul duality for Kac-Moody groups
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Bezrukavnikov_On Koszul.pdf
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1022.98 KB
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Author(s)
Bezrukavnikov, Roman
Yun, Zhiwei
Date Issued
January 2013
Journal
Representation Theory
Publisher
American Mathematical Society (AMS)
Citation
Bezrukavnikov, Roman, and Zhiwei Yun. “On Koszul Duality for Kac-Moody Groups.” Represent. Theory 17, no. 1 (January 2, 2013): 1–98.
Version
Author's final manuscript
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[superscript V]-monodromic mixed complexes on the enhanced flag variety G[superscript V]/U[superscript V], here G[superscript V] 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[superscript V]/B[superscript V]. 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].
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1090/S1088-4165-2013-00421-1
