On Koszul duality for Kac-Moody groups
Author(s)Bezrukavnikov, Roman; Yun, Zhiwei
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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].
DepartmentMassachusetts Institute of Technology. Department of Mathematics
American Mathematical Society (AMS)
Bezrukavnikov, Roman, and Zhiwei Yun. “On Koszul Duality for Kac-Moody Groups.” Represent. Theory 17, no. 1 (January 2, 2013): 1–98.
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