Equivariant Satake category and Kostant-Whittaker reduction

  title={Equivariant Satake category and Kostant-Whittaker reduction},
  author={Roman Bezrukavnikov and Michael Finkelberg},
  journal={arXiv: Representation Theory},
We explain (following V. Drinfeld) how the equivariant derived category of the affine Grassmannian can be described in terms of coherent sheaves on the Langlands dual Lie algebra equivariant with respect to the adjoint action, due to some old results of V. Ginzburg. The global cohomology functor corresponds under this identification to restricti on to the Kostant slice. We extend this description to loop rotation equivariant derived category, linking it to Harish-Chandra bimodules for the… 
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