Perverse Sheaves on Real Loop Grassmannians

2002/02/18 by David Nadler, Nadler, David · 3 citations
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #math.AG #math.RT

paper · pdf · doi:10.48550/arxiv.math/0202150

63 pages; final version, to appear in Invent math

openalex publication_date 2002/02/18 · arxiv created 2004/10/20 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Cited by

• Localizing invariants of constructible sheaves
• Matsuki correspondence for the affine Grassmannian
• Isotopy invariance and stratified 𝔼₂-structure of the Ran Grassmannian

Related

• Perverse Sheaves on Loop Grassmannians and Langlands Duality
• Perverse Sheaves on affine Grassmannians and Langlands Duality
• Reductive groups, the loop Grassmannian, and the Springer resolution
• On the action of the dual group on the cohomology of perverse sheaves on the affine grassmannian
• Geometric Langlands duality and forms of reductive groups