Spherical varieties and Langlands duality

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 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.

References in corpus (1)

• Electric-Magnetic Duality And The Geometric Langlands Program