Localization of \(\hat{\mathfrak{g}}\)-modules on the Affine Grassmannian

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Localization of \(\hat{\mathfrak{g}}\)-modules on the Affine Grassmannian

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Title: Localization of \(\hat{\mathfrak{g}}\)-modules on the Affine Grassmannian
Author: Frenkel, Edward; Gaitsgory, Dennis

Note: Order does not necessarily reflect citation order of authors.

Citation: Frenkel, Edward, and Dennis Gaitsgory. 2009. Localization of \(\hat{\mathfrak{g}}\)-modules on the affine Grassmannian. Annals of Mathematics 170(3): 1339-1381.
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Abstract: We consider the category of modules over the affine Kac-Moody algebra \(\hat{\mathfrak{g}}\) of critical level with regular central character. In our previous paper 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 \(I^0\) equivariant categories, where \(I^0\) 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 \(\mathfrak{g}\)-modules and D-modules on the flag variety \(G/B\), due to Beilinson-Bernstein and Brylinski-Kashiwara.
Published Version: doi://10.4007/annals.2009.170.1339
Other Sources: http://arxiv.org/abs/math/0512562v1
Terms of Use: This article is made available under the terms and conditions applicable to Open Access Policy Articles, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#OAP
Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:10043335
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