Local Geometric Langlands Correspondence: The Spherical Case

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Local Geometric Langlands Correspondence: The Spherical Case

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Title: Local Geometric Langlands Correspondence: The Spherical Case
Author: Frenkel, Edward; Gaitsgory, Dennis

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

Citation: Frenkel, Edward, and Dennis Gaitsgory. 2009. Local geometric langlands correspondence: The spherical case. In Algebraic analysis and around: In honor of Professor Masaki Kashiwara's 60th Birthday, ed. M. Kashiwara, T Miwa, et al, 167-186. Tokyo : Mathematical Society of Japan.
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Abstract: A module over an affine Kac–Moody algebra $\hat{g}$ is called spherical if the action of the Lie subalgebra g[[t]] on it integrates to an algebraic action of the corresponding group G[[t]]. Consider the category of spherical $\hat{g}$-modules of critical level. In this paper we prove that this category is equivalent to the category of quasi-coherent sheaves on the ind-scheme
of opers on the punctured disc which are unramified as local systems. This result is a categorical version of the well-known description of spherical vectors in representations of groups over local non-archimedian fields. It may be viewed as a special case of the local
geometric Langlands correspondence proposed in [FG2].
Published Version: http://mathsoc.jp/publication/ASPM/
Other Sources: http://arxiv.org/abs/0711.1132v1
Terms of Use: This article is made available under the terms and conditions applicable to Other Posted Material, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#LAA
Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:4341700
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