Spherical varieties and Langlands duality
| dc.creator | Gaitsgory, D. | |
| dc.creator | Nadler, D. | |
| dc.date | 2006-11-10 | |
| dc.date | 2007-08-07 | |
| dc.date.accessioned | 2026-07-07T08:22:28Z | |
| dc.date.available | 2026-07-07T08:22:28Z | |
| dc.description | Let G be a connected reductive complex algebraic group. This paper is devoted to the space Z of meromorphic quasimaps from a curve into an affine spherical G-variety X. The space Z may be thought of as an algebraic model for the loop space of X. In this paper, we associate to X a connected reductive complex algebraic subgroup $\check H$ of the dual group $\check G$. The construction of $\check H$ is via Tannakian formalism: we identify a certain tensor category Q(Z) of perverse sheaves on Z with the category of finite-dimensional representations of $\check H$. Combinatorial shadows of the group $\check H$ govern many aspects of the geometry of X such as its compactifications and invariant differential operators. When X is a symmetric variety, the group $\check H$ coincides with that associated to the corresponding real form of G via the (real) geometric Satake correspondence. | |
| dc.identifier | https://arxiv.org/abs/math/0611323 | |
| dc.identifier | http://arxiv.org/abs/math/0611323 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/135664 | |
| dc.subject | Representation Theory | |
| dc.subject | Algebraic Geometry | |
| dc.title | Spherical varieties and Langlands duality | |
| dc.type | text |