Perverse Sheaves on Real Loop Grassmannians

Details Perverse Sheaves on Real Loop Grassmannians Perverse Sheaves on Real Loop Grassmannians

2002-02-18

arxiv.org/abs/math/0202150v6

Mathematics

Algebraic Geometry

63 pages; final version, to appear in Invent math

Scientific paper

The aim of this paper is to identify a certain tensor category of perverse sheaves on the real loop Grassmannian of a real form $G_{\mathbb R}$ of a connected reductive complex algebraic group $G$ with the category of finite-dimensional representations of a connected reductive complex algebraic subgroup $\check H$ of the dual group $\check G$. The root system of $\check H$ is closely related to the restricted root system of the real form $G_{\mathbb R}$. The fact that $\check H$ is reductive implies that an interesting family of real algebraic maps satisfies the conclusion of the Decomposition Theorem of Beilinson-Bernstein-Deligne.

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