Localization of g-modules on the affine Grassmannian

• 成果类型: Article
• 署名作者: Frenkel, Edward; Gaitsgory, Dennis
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2009.170.1339
• 发表日期: 2009
• 页码: 1339-1381
• 关键词: kazhdan-lusztig conjecture; small quantum group; kac-moody algebras; lie-algebras; REPRESENTATIONS; LEVEL

摘要

We consider the category of modules over the affine Kac-Moody algebra 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 g-modules and D-modules on the flag variety G/B, due to Beilinson-Bernstein and Brylinski-Kashiwara.