Local Geometric Langlands Correspondence: the Spherical Case
| dc.creator | Frenkel, Edward | |
| dc.creator | Gaitsgory, Dennis | |
| dc.date | 2007-11-07 | |
| dc.date.accessioned | 2026-07-07T08:41:24Z | |
| dc.date.available | 2026-07-07T08:41:24Z | |
| dc.description | A module over an affine Kac--Moody algebra 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 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 arXiv:math/0508382. | |
| dc.description | 14 pages | |
| dc.identifier | https://arxiv.org/abs/0711.1132 | |
| dc.identifier | http://arxiv.org/abs/0711.1132 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/141662 | |
| dc.subject | Quantum Algebra | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Representation Theory | |
| dc.title | Local Geometric Langlands Correspondence: the Spherical Case | |
| dc.type | text |