Hecke operators on quasimaps into horospherical varieties
| dc.creator | Gaitsgory, D. | |
| dc.creator | Nadler, D. | |
| dc.date | 2004-11-11 | |
| dc.date | 2006-11-10 | |
| dc.date.accessioned | 2026-07-07T06:38:59Z | |
| dc.date.available | 2026-07-07T06:38:59Z | |
| dc.description | Let $G$ be a connected reductive complex algebraic group. This paper is part of a project 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 $X$. The theory we develop associates 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. In this paper, we focus on horospherical varieties, a class of varieties closely related to flag varieties. | |
| dc.description | 27 pages | |
| dc.identifier | https://arxiv.org/abs/math/0411266 | |
| dc.identifier | http://arxiv.org/abs/math/0411266 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/100936 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Representation Theory | |
| dc.title | Hecke operators on quasimaps into horospherical varieties | |
| dc.type | text |