Equivariant Satake category and KostantWhittaker 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 HarishChandra bimodules for the Langlands dual Lie algebra, so that the global cohomology functor corresponds to the quantum KostantWhittaker reduction of a HarishChandra bimodule. We derive a conjecture from math.AG/0306413 which identifies the looprotation equivariant homology of the affine Grassmannian with quantized completed Toda lattice.
 Publication:

arXiv eprints
 Pub Date:
 July 2007
 arXiv:
 arXiv:0707.3799
 Bibcode:
 2007arXiv0707.3799B
 Keywords:

 Mathematics  Representation Theory
 EPrint:
 31 pages, to appear in Moscow Math J