Perverse sheaves on real loop Grassmannians

• 成果类型: Article
• 署名作者: Nadler, D
• 署名单位: University of Chicago
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-004-0382-3
• 发表日期: 2005
• 页码: 1-73
• 关键词: hopf-algebras; bundles; FORMULA; CURVES; MODULI

摘要

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