On Koszul duality for Kac-Moody groups

By R. Bezrukavnikov, Zhiwei Yun. 2011

106 citations recorded by the source corpus.

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 $B^\vee$-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 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 the work of Beilinson, Ginzburg and Soergel .

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/064a0aa0475d2cc7efc546d33ec2346f4d4c3988

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In Discrete Mathematics and Combinatorics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

On two geometric realizations of an affine Hecke algebra (2012, methodology): “on GF/(I0)′ which are ψ -equivariant with respect to the right action of I0/(I0)′, this is a particular case of the category considered in [23] (again, one needs to switch left with right to get from the present setting to that of [23]).”