LOCALIZATION OF ĝ–MODULES ON THE AFFINE GRASSMANNIAN
نویسنده
چکیده
We consider the category of modules over the affine Kac-Moody algebra ĝ of critical level with regular central character. In our previous paper [FG2] we conjectured that this category is equivalent to the category of Hecke eigen-D-modules on the affine Grassmannian G((t))/G[[t]]. This conjecture was motivated by our proposal for a local geometric Langlands correspondence. In this paper we prove this conjecture for the corresponding I-equivariant categories, where I is the radical of the Iwahori subgroup of G((t)). Our result may be viewed as an affine analogue of the equivalence of categories of g-modules and D-modules on the flag variety G/B, due to Beilinson-Bernstein and Brylinski-Kashiwara.
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