Equivariant Satake category and Kostant-Whittaker reduction
Abstract
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 Langlands dual Lie algebra, so that the global cohomology functor corresponds to the quantum Kostant-Whittaker reduction of a Harish-Chandra bimodule. We derive a conjecture from math.AG/0306413 which identifies the loop-rotation equivariant homology of the affine Grassmannian with quantized completed Toda lattice.
Cite
@article{arxiv.0707.3799,
title = {Equivariant Satake category and Kostant-Whittaker reduction},
author = {Roman Bezrukavnikov and Michael Finkelberg},
journal= {arXiv preprint arXiv:0707.3799},
year = {2026}
}
Comments
This version corrects a mistake in the proof of Theorem 1b) and a typo in Proposition 7. All the statements are unchanged from the previous version. We thank Jakub L\"owut for pointing out the issue in Theorem 1b)