Local geometric Langlands correspondence and affine Kac-Moody algebras
| dc.creator | Frenkel, Edward | |
| dc.creator | Gaitsgory, Dennis | |
| dc.date | 2005-08-20 | |
| dc.date | 2006-07-11 | |
| dc.date.accessioned | 2026-07-07T06:42:49Z | |
| dc.date.available | 2026-07-07T06:42:49Z | |
| dc.description | By a local geometric Langlands correspondence for a complex reductive group G we understand a construction which assigns to a local system on the punctured disc for the Langlands dual group of G, a category equipped with an action of the formal loop group G((t)). We propose a conjectural description of these categories as categories of representations of the corresponding affine Kac-Moody algebra of critical level, and, in some cases, as categories of D-modules on the ind-schemes G((t))/K. We describe in detail these categories and interrelations between them and provide supporting evidence for our conjectures. In particular, we prove that a certain quotient category of representations of critical level is equivalent to the category of quasicoherent sheaves on a thickening of the scheme of nilpotent opers associated to the Langlands dual group. | |
| dc.description | 156 pages | |
| dc.identifier | https://arxiv.org/abs/math/0508382 | |
| dc.identifier | http://arxiv.org/abs/math/0508382 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/102182 | |
| dc.subject | Representation Theory | |
| dc.subject | High Energy Physics - Theory | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Quantum Algebra | |
| dc.title | Local geometric Langlands correspondence and affine Kac-Moody algebras | |
| dc.type | text |