Spherical varieties and Langlands duality-猫眼课题宝

球形簇和朗兰兹对偶性

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2006

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作者：

D. Gaitsgory;D. Nadler;Pierre Deligne;D. Nadler

设$G$是一个连通的约化复代数群。本文致力于研究从一条曲线到一个仿射球形$G$-簇$X$的亚纯拟映射的空间$Z$。空间$Z$可被视为$X$的环路空间的一个代数模型。在本文中，我们给$X$关联对偶群$\check{G}$的一个连通的约化复代数子群$\check{H}$。$\check{H}$的构造是通过坦纳凯恩形式主义：我们将$Z$上的某个反常层的张量范畴$Q(Z)$与$\check{H}$的有限维表示范畴等同起来。群$\check{H}$的组合影子支配着$X$的几何的许多方面，例如它的紧化和不变微分算子。当$X$是一个对称簇时，群$\check{H}$与通过（实）几何萨塔克对应关联到$G$的相应实形式的群一致。

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.

Spherical varieties and Langlands duality

球形簇和朗兰兹对偶性

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