This article is cited in 26 papers

Spherical varieties and Langlands duality

Dennis Gaitsgory^a, David Nadler<sup>b

a</sup> Department of Mathematics, Harvard University, Cambridge, MA
^b Department of Mathematics, Northwestern University, Evanston, IL

Abstract: 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 a finite-dimensional 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 $\mathbf Q(Z)$ of perverse sheaves on $Z$ with the category of finite-dimensional representations of $\check H$. The group $\check H$ encodes many aspects of the geometry of $X$.

Key words and phrases: loop spaces, Langlands duality, quasimaps.

MSC: Primary 22E67; Secondary 14H60, 55P35

Received: April 27, 2008

Language: English

DOI: 10.17323/1609-4514-2010-10-1-65-137

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