Local Geometric Langlands Correspondence: The Spherical Case
| 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. |
| Full Text & Related Files: |
Frenkel_LocalGeometric.pdf (237.0Kb; PDF) 
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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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